Department of Physics, Unit Catalogue 2004/05 
PH10001: Introduction to quantum physics 
Credits: 6 
Level: Certificate 
Semester: 1 
Assessment: EX80CW20 
Requisites: 
Students must have Alevel Physics and Mathematics to undertake this unit.
Aims & Learning Objectives: The aims of this unit are to review the evidence for the existence of atoms and the scientific developments which reveal the breakdown of classical physics at the atomic level, and to introduce the ideas of energy and angular momentum quantisation and the dual waveparticle nature of matter. After taking this unit the student should be able to * identify the historical evidence for the atomic nature of matter * describe the Bohr, Thomson and Rutherford models of the atom and the origin of quantisation of energy * discuss the concepts of wave/particle duality, probability distributions and wavefunctions * perform simple calculations on atomic line spectra Content: The constituents of the atom: Quantum and classical domains of physics. Existence of atoms. Avogadro's number. Electrons and ions. The mass spectrograph. Atomic mass units. Structure of atoms; scattering of alphaparticles and Rutherford's model. Photons and energy quantisation: Blackbody radiation; the ultraviolet catastrophe and Planck's hypothesis. Photoelectric effect. The electromagnetic spectrum. Xrays. Compton scattering. Sources of photons; the Bohr model of the atom. Deficiencies of Bohr's model. Waveparticle duality: An introduction to waves. Wavelike properties of photons and other particles; inadequacies of classical models. De Broglie's hypothesis. Electron diffraction. Wave aspects of larger particles; atoms, molecules, neutrons. The uncertainty principle. Introduction to quantum mechanics: Probability distributions. Introduction to Schrodinger's wave equation. Normalisation of wave functions and expectation values of position. 
PH10002: Properties of matter 
Credits: 6 
Level: Certificate 
Semester: 1 
Assessment: EX80CW20 
Requisites: 
Students must have Alevel Physics or Chemistry and Alevel Mathematics to undertake this unit.
Aims & Learning Objectives: The aims of this unit are to gain insight into how the interplay between kinetic and potential energy at the atomic level governs the formation of different phases and to demonstrate how the macroscopic properties of materials can be derived from considerations of the microscopic properties at the atomic level. After taking this unit the student should be able to: * use simple model potentials to describe molecules and solids; * solve simple problems for ideal gases using kinetic theory; * describe the energy changes in adiabatic and isothermal processes; * derive thermodynamic relationships and analyse cycles; * derive and use simple transport expressions in problems concerning viscosity, heat and electrical conduction. Content: Balance between kinetic and potential energy. The ideal gas  Kinetic Theory; Maxwell Boltzmann distribution; Equipartition. The real gas  van der Waals model. The ideal solid  model potentials and equilibrium separations of molecules and Madelung crystals. Simple crystal structures, Xray scattering and Bragg's law. First and second laws of thermodynamics, PVT surfaces, phase changes and critical points, thermodynamic temperature and heat capacity of gases. Derivation of mechanical (viscosity, elasticity, strength, defects) and transport properties (heat and electrical conduction) of gases and solids from considerations of atomic behaviour. Qualitative understanding of viscosity (Newtonian and nonNewtonian) in liquids based on cage models. 
PH10003: Introduction to electronics 
Credits: 6 
Level: Certificate 
Semester: 1 
Assessment: EX80CW20 
Requisites: 
While taking this unit you must take PH10007 
Aims & Learning Objectives: The aim of this unit is to provide an introduction to electronics by developing an understanding of basic concepts in dc and ac electric circuits and digital electronics. After taking this unit the student should be able to: * use a systematic analysis method (e.g. nodal voltage) to calculate currents and voltages in passive dc circuits * calculate the amplitude and phase of voltages and currents in ac circuits by means of phasor analysis * analyse simple operational amplifier circuits from first principles * analyse simple logic circuits containing gates and flipflops * use Boolean algebra and Karnaugh maps to simplify logic expressions * design logic circuits to implement basic tasks. Content: DC Circuits: Kirchoff's voltage and current laws. Ideal voltage and current sources. Analysis of simple circuits using nodal voltage technique. Equivalent circuits. Thevenin and Norton theorems. Impedance matching  input/output impedance, maximum power transfer, maximum voltage transfer. (5 lectures). Diode Circuits: Diode models: oneway valve, piecewise linear and general form of diode equation. Load lines. Applications, including rectifiers, clamps and Zener regulation. (1 lecture). AC Circuits: AC voltage and current concepts (phase, rms value, amplitude etc.). Capacitors and inductors as circuit elements. Phasors and phasor notation. Complex impedance. LCR circuits (resonance, Q factor etc). Frequency dependence of circuits, RC filters. Bode plots. (5 lectures). Operational Amplifiers and feedback: Theory of ideal operational amplifiers. Simple applications e.g. inverting, noninverting and differential amplifiers, addition and subtraction, differentiation, integration, buffer amplifiers. Blackbox treatment of amplifiers; input, output and transfer characteristics. Characteristics of ideal and real opamps. Effect of finite gain and bandwidth. Negative feedback systems and advantages of negative feedback. Positive feedback for oscillators. (3 lectures). Transients: Techniques for solving for transient waveforms in simple circuits involving inductors, capacitors, resistors and opamps. (1 lecture). Digital electronics: Digital and analog electronics. Combinational logic. Representation of logic levels. AND, OR and NOT gates. Truth tables. XOR, NAND and NOR. Boolean algebra: Notation, laws, identities and De Morgan's Laws. Standard sum of products. Manipulation between forms. Karnaugh maps: 2,3 and 4 variables. Simplification. Logic gates and characteristics, logic family characteristics: Fan out, noise margin and propagation delay. Combinational functions: decoder, encoder, ROM structure. Sequential logic: latch, SR flipflop and JK flipflop. Shift register. Ripple counter. (8 lectures). DigitaltoAnalogue and AnaloguetoDigital Converters: Binary weighted and R2R DACs. Flash ADCs. (1 lecture). 
PH10004: Relativity & astrophysics 
Credits: 6 
Level: Certificate 
Semester: 2 
Assessment: EX80CW20 
Requisites: 
Students must have Alevel Physics and Mathematics to undertake this unit.
Aims & Learning Objectives: The aims of this unit are to introduce the concepts and results of special relativity and to provide a broad introduction to astronomy and astrophysics. An additional aim is that the student's appreciation of important physical phenomena such as gravitation and blackbody radiation should be reinforced through their study in astrophysical contexts. After taking this unit, the student should be able to: * write down the essential results and formulae of special relativity; * describe the important special relativity experiments (real or thought); * solve simple kinematic and dynamical special relativity problems; * give a qualitative account of how the sun and planets were formed; * describe how stars of differing masses evolve; * give a simple description of the expanding Universe and its largescale structure; * solve simple problems concerning orbital motion, blackbody radiation, cosmological redshift, stellar luminosity and magnitude. Content: Special Relativity: Galilean transformation. Speed of light  MichelsonMorley experiment; Einstein's postulates. Simultaneity; time dilation; space contraction; invariant intervals; rest frames; proper time; proper length. Lorentz transformation. Relativistic momentum, force, energy. Doppler effect. Astrophysical Techniques: Telescopes and detectors. Invisible astronomy : Xrays, gammarays, infrared and radio astronomy. Gravitation: Gravitational force and potential energy. Weight and mass. Circular orbits; Kepler's Laws; planetary motion. Escape velocity. Solar System: EarthMoon system. Terrestrial planets; Jovian planets. Planetary atmospheres. Comets and meteoroids. Formation of the solar system. The interstellar medium and star birth. Stellar distances, magnitudes, luminosities; blackbody radiation; stellar classification; HertzsprungRussell diagram. Stellar Evolution: Star death: white dwarfs, neutron stars. General Relativity: Gravity and geometry. The principle of equivalence. Deflection of light; curvature of space. Gravitational time dilation. Red shift. Black holes. Large scale structure of the Universe. Galaxies: Galactic structure; classification of galaxies. Formation and evolution of galaxies. Hubble's Law. The expanding universe. The hot Big Bang. Cosmic background radiation and ripples therein. 
PH10005: Mechanics & waves 
Credits: 6 
Level: Certificate 
Semester: 2 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH10007 
Aims & Learning Objectives: The aims of this unit are to present students with a clear and logical guide to classical mechanics, to strengthen their understanding of mechanics by means of practical problems and to introduce them to the fundamental concepts and mathematical treatment of waves. After taking this unit the student should be able to: * apply Newton's laws to solve simple real world problems and gain insight into microscopic processes at the atomic level; * use vector notation and methods to solve problems in rotational dynamics; * analyse oscillating systems under different driving regimes; * apply the wavefunction for a onedimensional travelling wave to problems involving mechanical, acoustic, water and electromagnetic waves; * define and derive the impedance of a mechanical wave and apply it to reflection and transmission at interfaces; * analyse interference and diffraction arising from simple onedimensional structures; * derive and apply the formulae for the nonrelativistic Doppler effect. Content: Dimensions and Units: fundamental SI units, measurement standards, dimensional analysis. Newton's Laws of Motion: Motion in 1D and 2D with constant and nonconstant acceleration. Linear momentum, collisions, rockets. Work and Energy: potential energy, conservative and nonconservative forces. Circular motion: Rigid body rotation: moments of inertia; torque and angular momentum as vectors; equations of motion of rotating bodies; gyroscopes. Simple Harmonic Motion: including damped, forced; resonance. Coupled oscillations and introduction to normal modes. Travelling waves: strings, sound, water, particle and light waves. Mathematical representation: sinusoidal waves; amplitude, frequency, wavelength, wavenumber, speed, energy, intensity and impedance. General differential equation for 1D wave. Complex exponential notation. Superposition: Wave interference, reflection and transmission at boundaries. Dispersive and nondispersive waves, phase and group velocity. Beats. Doppler effect. 
PH10006: Electricity & magnetism 
Credits: 6 
Level: Certificate 
Semester: 2 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH10007 
Aims & Learning Objectives: The aims of this unit are to introduce the fundamental laws of electricity and magnetism and to develop techniques used in the solution of simple field problems, both vector and scalar. After taking this unit the student should be able to: * state the basic laws of electricity and magnetism; * define scalar and vector fields and represent them graphically; * determine the forces due to electric and magnetic fields acting on charges and currents; * determine electric fields, potentials and energies due to simple, static charge distributions; * determine magnetic fields and energies due to simple, steady current distributions; * determine electric fields, e.m.f.s and induced currents due to varying magnetic fields. Content: Introduction to scalar and vector fields. Electrostatics: Electric charge, Coulomb's Law, superposition of forces, electric charge distribution, the electric field, electric flux, Gauss's Law, examples of field distributions, electric dipoles. Line integral of the electric field, potential difference, calculation of fields from potential, examples of potential distributions, energy associated with electric field. Electric field around conductors, capacitors and their capacitance, energy stored. Magnetism: Lorentz force law, force on a currentcarrying wire, force between currentcarrying wires, torque on a current loop, magnetic dipoles. BiotSavart Law, Ampere's Law, magnetic flux, Gauss's Law in magnetism, examples of field distributions. Electromagnetic Induction: Induced e.m.f. and examples, Faraday's Law, Lenz's Law, energy stored in a magnetic field, self and mutual inductance, energy stored in an inductor. 
PH10007: Mathematics for scientists 1 
Credits: 6 
Level: Certificate 
Semester: 1 
Assessment: EX80CW20 
Requisites: 
Students must have Alevel Mathematics to undertake this unit.
Aims & Learning Objectives: The aim of this unit is to introduce basic mathematical techniques required by science students, both by providing a reinterpretation of material already covered at Alevel in a more general and algebraic form and by introducing more advanced topics. After taking this unit the student should be able to: * sketch graphs of standard functions and their inverses; * represent complex numbers in cartesian, polar and exponential forms, and convert between these forms; * calculate the magnitude of a vector, and the scalar and vector products of two vectors; * solve standard geometrical problems involving vectors; * evaluate the derivative of a function and the partial derivative of a function of two or more variables; * write down the Taylor series approximation to a function. Content: Functions of a real variable (3 hours): Graphs of standard functions (polynomial, exponential, logarithmic, trigonometric and hyperbolic functions). Domains and ranges. Composite functions. Inverse functions. Symmetries and transformations (reflections, rotation) of graphs. Polynomial curve fitting. Complex numbers (4 hours): Definition and algebra of complex numbers in x+iy form. Complex conjugate. Modulus and argument. Argand diagram, re^{iθ} form. De Moivre's theorem. Solution of equations involving complex variables. Vector algebra (7 hours): Introduction to vectors; physical examples of scalar and vector quantities. Magnitude of a vector, unit vector. Cartesian components. Scalar product; projections, components, physical examples. Vector product; determinantal form for Cartesian components, physical examples. Geometrical applications of vectors. Triple product. Introduction to vector spaces. Differentiation (10 hours): Limits and continuity, differentiability. Review of differentiation. Higher derivatives, meaning of derivatives. Graphical interpretation of derivatives. Logarithmic, parametric and implicit derivatives. Taylor and Maclaurin expansions; remainder terms. Standard series. Convergence of series; ratio test, limits, L'Hopital's rule. Functions of two variables. Partial differentiation. Taylor expansion in two variables. Chain rule. Small changes and differentials, total derivative. 
PH10008: Mathematics for scientists 2 
Credits: 6 
Level: Certificate 
Semester: 2 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH10007 
Aims & Learning Objectives: The aim of this unit is to introduce basic mathematical techniques required by science students, both by providing a reinterpretation of material already covered at Alevel in a more general and algebraic form and by introducing more advanced topics. After taking this unit the student should be able to: * integrate functions using a variety of standard techniques; * find the general solution to first and second order ordinary differential equations and show how a particular solution may be found using boundary conditions; * describe the form of the general solution of partial differential equations; * solve some first and second order partial differential equations by means of separation of variables; * calculate the determinant and inverse of a matrix, and evaluate the product of two matrices; * use matrix methods to solve simple linear systems. Content: Integration (7 hours): Review of integration. Meaning of integration. Methods of integration. Multiple integral, change of order of integration. Applications of integration (area, volume, etc). Numerical integration methods. Ordinary differential equations (8 hours): Origin of ODEs. Solution of first order ODEs by integrating factors and separation of variables. Solution of second order ODEs with constant coefficients. Complementary functions and particular integral. Applications in the natural sciences; rate equations, population dynamics, oscillatory systems, etc. Numerical solution of ODEs; Euler method, RungeKutta methods. Introduction to partial differential equations (3 hours): Origin of PDEs. Solution of PDEs by separation of variables. Wave equation in one dimension. Matrices and determinants (6 hours): Introduction to matrices. Special matrices. Transpose of a matrix. Matrix multiplication. Linear transformations. Introductions to determinants. Inverse of a matrix. Simultaneous linear equations. Solution of simultaneous equations; Gaussian elimination. 
PH10011: Laboratory & information skills  1A 
Credits: 6 
Level: Certificate 
Semester: 1 
Assessment: PR90CW10 
Requisites: 
After taking this unit you must take PH10012 
Aims & Learning Objectives: The primary aims of this unit are to give the student confidence and competence in basic laboratory and information processing skills, and to introduce laboratory project work. A further aim is to reinforce other course material through selfpaced laboratory demonstrations. While taking this unit the student should be able to: * demonstrate the correct use of common laboratory equipment, such as oscilloscopes, multimeter, digital timer/counters and optical detectors; * correctly follow written instructions for setting up and carrying out experimental demonstrations in various topics relating to level 1, semester 1 physics modules; * use a scientific log book for recording details of experimental procedure, experimental results and data analysis; * plan, design and carry out a physics project consisting of a smallscale experimental investigation in one of various topics relating to major areas of physics; * use computer software packages for word processing, spreadsheet and data analysis to write a formal scientific project report. Content: Techniques of measurement: Use of multimeters, oscilloscope, protoboard, operational amplifier and digital timer/counter; mechanical measurements, light sources and detectors. Demonstrations: RC networks, series resonance, statistics of radiation counting. Elastic properties, fluid flow. Electronics: Characteristics and applications of basic combinatorial and sequential logic elements. Projects: An independent project to simulate the processes of researching, planning, performing, analysing and reporting a smallscale experimental investigation. The topic is chosen from a wide range of physics appropriate to firstyear students, including hypothesis testing, design of apparatus, assessing published proposals and investigating novel phenomena. Supporting Lectures and PC Laboratory Sessions: The use of logarithmic scales for graphing experimental data, statistical treatment of random error and variation; mean, standard deviation, standard error, confidence limits, linear regression. Intro to PC's, Windows, word processing. The use of spreadsheets, such as EXCEL to perform statistical operations and data analysis. The use of word processors, such as WORD to produce technical reports. The use of information technology and services for scientific purposes, including email, internet resources, library Unicorn system. 
PH10012: Laboratory & information skills  1B 
Credits: 6 
Level: Certificate 
Semester: 2 
Assessment: PR80OT20 
Requisites: 
Before taking this unit you must take PH10011 
Aims & Learning Objectives: The aim of this unit is to build on the basic laboratory skills developed in PH10011, extending the scope of the demonstrations and project work. Two additional aims are to introduce the use of computer software to simulate electrical circuits, and to give students experience of presenting their work in the form of a poster. While taking this unit the student should be able to: * build simple electronic circuits involving operational amplifiers; * correctly follow written instructions for setting up and carrying out experimental demonstrations in various topics related to level 1, semester 2 physics modules; * plan, design and carry out a physics project consisting of a smallscale experimental investigation in one of various topics relating to major areas of physics, this project to be of a more challenging nature than that carried out in PH10011; * build an electronic circuit using basic logic components to perform a simple task; * design and make a poster based on the physics project, and present this at an open poster presentation; * use a computer software package to simulate the operation of passive networks and compare the results with the measured behaviour. Content: Techniques: Operational amplifiers. Demonstrations: Ultrasonic waves in air. The Michelson Interferometer. Vibrations of strings. Diffraction, equipotentials & field lines. Electronics: Miniproject to design, construct and test a basic digital system. Project: A second independent project, similar in nature to that in PH10011. The students' second project is reported in writing and in the form of a Poster Presentation, in the style of conference posters. This will be judged by all staff and students at an open evening presentation. PC Laboratory Sessions: Scientific Computer Packages  Circuit simulation. Standard computer software is used to simulate the behaviour of simple, passive, electrical circuits. The simulation is tested against measured behaviour. 
PH10048: Introduction to quantum physics [WL] 
Credits: 6 
Level: Certificate 
Semester: 1 
Assessment: CW20EX67PR13 
Requisites: 
While taking this unit you must take PH10007 and take PH10053 and in taking this unit you cannot take PH10001 
Students must have Alevel Physics and Alevel Mathematics in order to undertake this unit. Those students without Alevel Mathematics must take PH10007.
Aims & Learning Objectives: The aims of this unit are to review the evidence for the existence of atoms and the scientific developments which reveal the breakdown of classical physics at the atomic level, and to introduce the ideas of energy and angular momentum quantisation and the dual waveparticle nature of matter. A further aim is to give students confidence and competence in basic laboratory skills. After taking this unit the student should be able to: * identify the historical evidence for the atomic nature of matter; * describe the Bohr, Thomson and Rutherford models of the atom and the origin of quantisation of energy; * discuss the concepts of wave/particle duality, probability distributions and wavefunctions; * perform simple calculations on atomic line spectra; * explain the origin of the periodic table; * demonstrate the correct use of common laboratory equipment, maintain a scientific logbook and perform basic error analysis. Content: The constituents of the atom: Quantum and classical domains of physics. Existence of atoms. Avogadro's number. Electrons and ions. The mass spectrograph. Atomic mass units. Structure of atoms; scattering of alphaparticles and Rutherford's model. Photons and energy quantisation: Blackbody radiation; the ultraviolet catastrophe and Planck's hypothesis. Photoelectric effect. The electromagnetic spectrum. Xrays. Compton scattering. Sources of photons; the Bohr model of the atom. Deficiencies of Bohr's model. Waveparticle duality: An introduction to waves. Wavelike properties of photons and other particles; inadequacies of classical models. De Broglie's hypothesis. Electron diffraction. Electron microscopy. Wave aspects of larger particles; atoms, molecules, neutrons. The uncertainty principle. Introduction to quantum mechanics: Probability distributions. Introduction to Schrodinger's wave equation. Energy levels for hydrogen. Quantum numbers. Electron spin. The exclusion principle. The periodic table. Optical and Xray spectra. Shells, valency and chemical bonding. Practical laboratory: Performance of experiments designed to develop practical skills and support lecture material. 
PH10051: Electricity & magnetism [WL] 
Credits: 6 
Level: Certificate 
Semester: 2 
Assessment: CW20EX67PR13 
Requisites: 
While taking this unit you must take PH10008 and before taking this unit you must take PH10007 and take PH10052 and in taking this unit you cannot take PH10006 
Students must have Alevel physics in order to take this unit.
Aims & Learning Objectives: The aims of this unit are to introduce the fundamental laws of electricity and magnetism and to develop techniques used in the solution of simple field problems, both vector and scalar. A further aim is to develop students confidence and competence in basic laboratory skills. After taking this unit the student should be able to: * state the basic laws of electricity and magnetism; * define scalar and vector fields and represent them graphically; * determine the forces due to electric and magnetic fields acting on charges and currents; * determine electric fields, potentials and energies due to simple, static charge distributions; * determine magnetic fields and energies due to simple, steady current distributions; * determine electric fields, e.m.f.s and induced currents due to varying magnetic fields; * demonstrate the correct use of a wider range of common laboratory equipment, maintain a scientific logbook and produce a scientific report. Content: Introduction to scalar and vector fields. Electrostatics: Electric charge, Coulomb's Law, superposition of forces, electric charge distribution, the electric field, electric flux, Gauss's Law, examples of field distributions, electric dipoles. Line integral of the electric field, potential difference, calculation of fields from potential, examples of potential distributions, energy associated with electric field. Electric field around conductors, capacitors and their capacitance, energy stored. Magnetism: Lorentz force law, force on a currentcarrying wire, force between currentcarrying wires, torque on a current loop, magnetic dipoles. BiotSavart Law, Ampere's Law, magnetic flux, Gauss's Law in magnetism, examples of field distributions. Electromagnetic Induction: Induced e.m.f. and examples, Faraday's Law, Lenz's Law, energy stored in a magnetic field, self and mutual inductance, energy stored in an inductor. Practical laboratory: Performance of experiments designed to develop practical skills and support lecture material. 
PH10052: Properties of matter [WL] 
Credits: 6 
Level: Certificate 
Semester: 1 
Assessment: CW20EX67PR13 
Requisites: 
While taking this unit you must take PH10007 and take PH10051 and in taking this unit you cannot take PH10002 
Students must have Alevel Physics or Chemistry and Alevel Mathematics to undertake this unit.
Aims & Learning Objectives: The aims of this unit are to gain insight into how the interplay between kinetic and potential energy at the atomic level governs the formation of different phases and to demonstrate how the macroscopic properties of materials can be derived from considerations of the microscopic properties at the atomic level. A further aim is to give students confidence and competence in basic laboratory skills. After taking this unit the student should be able to: * use simple model potentials to describe molecules and solids; * solve simple problems for ideal gases using kinetic theory; * describe the energy changes in adiabatic and isothermal processes; * derive thermodynamic relationships and analyse cycles; * derive and use simple transport expressions in problems concerning viscosity, heat and electrical conduction; * demonstrate the correct use of common laboratory equipment, maintain a scientific logbook and produce an outline scientific report. Content: Balance between kinetic and potential energy. The ideal gas  Kinetic Theory; Maxwell Boltzmann distribution; Equipartition. The real gas  van der Waals model. The ideal solid  model potentials and equilibrium separations of molecules and Madelung crystals. Simple crystal structures, Xray scattering and Bragg's law. First and second laws of thermodynamics, PVT surfaces, phase changes and critical points, thermodynamic temperature and heat capacity of gases. Derivation of mechanical (viscosity, elasticity, strength, defects) and transport properties (heat and electrical conduction) of gases and solids from considerations of atomic behaviour. Qualitative understanding of viscosity (Newtonian and nonNewtonian) in liquids based on cage models. Practical laboratory: Performance of experiments designed to develop practical skills and support lecture material. 
PH10053: Mechanics & waves [WL] 
Credits: 6 
Level: Certificate 
Semester: 2 
Assessment: CW20EX67PR13 
Requisites: 
Before taking this unit you must take PH10007 and take PH10048 and while taking this unit you must take PH10008 and in taking this unit you cannot take PH10005 
Aims & Learning Objectives: The aims of this unit are to present students with a clear and logical guide to classical mechanics, to strengthen their understanding of mechanics by means of practical problems and to introduce them to the fundamental concepts and mathematical treatment of waves. A further aim is to develop students confidence and competence in basic laboratory skills. After taking this unit the student should be able to: * apply Newton's laws to solve simple real world problems and gain insight into microscopic processes at the atomic level: * use vector notation and methods to solve problems in rotational dynamics; * analyse oscillating systems under different driving regimes; * apply the wavefunction for a onedimensional travelling wave to problems involving; mechanical, acoustic, water and electromagnetic waves; * define and derive the impedance of a mechanical wave and apply it to reflection and transmission at interfaces; * analyse interference and diffraction arising from simple onedimensional structures * derive and apply the formulae for the nonrelativistic Doppler effect; * demonstrate the correct use of a wider range of common laboratory equipment, maintain a scientific logbook and perform basic data analysis. Content: Dimensions and Units: fundamental SI units, measurement standards, dimensional analysis. Newton's Laws of Motion: Motion in 1D and 2D with constant and nonconstant acceleration. Linear momentum, collisions, rockets. Work and Energy: potential energy, conservative and nonconservative forces. Circular motion: Rigid body rotation: moments of inertia; torque and angular momentum as vectors; equations of motion of rotating bodies; gyroscopes. Simple Harmonic Motion: including damped, forced; resonance. Coupled oscillations and introduction to normal modes. Travelling waves: strings, sound, water, particle and light waves. Mathematical representation: sinusoidal waves; amplitude, frequency, wavelength, wavenumber, speed, energy, intensity and impedance. General differential equation for 1D wave. Complex exponential notation. Superposition: Wave interference, reflection and transmission at boundaries. Dispersive and nondispersive waves, phase and group velocity. Beats. Michelson interferometer. Doppler effect. Practical laboratory: Performance of experiments designed to develop practical skills and support lecture material. 
PH20013: Quantum & atomic physics 
Credits: 6 
Level: Intermediate 
Semester: 1 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must (take PH10001 and take PH10008) or take PH10048 
Natural science students must have taken PH10048 in order to undertake this unit.
PH10001 and PH10005 are desirable as prerequisites but not essential.
Aims & Learning Objectives: The aims of this module are to introduce the Schrodinger wave equation and its solution in one and three dimensions, and to explore the interactions responsible for the electronic structure of atoms. After taking this unit the student should be able to: * explain the significance of the wavefunction in determining the physical behaviour of electrons; * show how quantisation arises from boundary conditions; * calculate energy levels in simple model systems; * outline the quantum mechanical description of the hydrogen atom; * discuss the energy levels, angular momenta and spectra of simple atoms, taking into account screening, magnetic interactions and the exchange interaction; * make simple quantitative estimates of magnetic energies in atoms; * use empirical rules to establish the ground state terms and configurations of atoms. Content: Basic assumptions of quantum mechanics: wave functions and probability density. Observables; position, momentum and energy. Schrodinger equation: time dependence of the wave function. Timeindependent Schrodinger equation and stationary states. Motion in one dimension: the infinite square well; bound state energies and wave functions. Parity of solutions. Motion of free particles. Reflection and transmission at a potential step. Bound states of a finite square well. Tunnelling through a barrier. The harmonic oscillator. Motion in three dimensions: central potentials. Angular dependence of solutions. Angular momentum quantum numbers; s, p and d states. Spin angular momentum. Vector model of the atom. Orbital and spin magnetic moments and their coupling in a one electron atom. Fine structure in hydrogen. Factors affecting intensity of spectral lines. Effect of the nuclear magnetic moment on atomic spectra: hyperfine structure, nuclear magnetic resonance. Atoms with more than one electron: Pauli exclusion principle and shell structure. Electronelectron interactions: screening and exchange interaction. Chemical bonding. Nomenclature for labelling atomic configurations and terms. Hund's rules. Fine structure and Zeeman effect in manyelectron atoms. Factors affecting width of spectral lines and introduction to high resolution spectroscopy. 
PH20014: Electromagnetic waves & optics 
Credits: 6 
Level: Intermediate 
Semester: 2 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must (take PH10008 and take PH10005 and take PH10006) or (take PH10051 and take PH10053) 
Natural science students must have taken PH10051 and PH10053 in order to undertake this unit.
PH10005 and PH10006 are desirable, but not essential, prerequisites for this unit.
Aims & Learning Objectives: The aims of this unit are to introduce the properties of electromagnetic plane waves, to provide a mathematical framework for the understanding of the wave nature of light and to describe the properties of simple optical devices. After taking this unit the student should be able to: * list the distinguishing features of electromagnetic plane waves and write down a mathematical expression for a linearly or circularly polarised light wave; * construct ray diagrams for use in solving simple geometrical optics problems; * outline the mathematical analysis of multiplebeam interference and hence interpret the output from a FabryPirot interferometer; * discuss the concept of coherence with regard to the physical properties of the source and the effect of partial coherence on fringe visibility; * derive mathematical expressions for simple diffraction patterns and relate the limits imposed by diffraction to the performance of optical instruments; * describe how lasing action is obtained and maintained and outline the main properties of laser light. Content: Electromagnetic plane waves: The em spectrum; sources and production of light; wave and photon description; the optical region; Revision of 1D waves. 3D plane waves, vector nature of em waves; relationships between E B and k. Polarisation. Methods of obtaining linearly polarised light, Law of Malus. Circular and elliptical polarisation. Energy and the Poynting vector. Impedance. Phase velocity, permittivity, permeability. Refractive index and its microscopic origin. Concept of birefringence. Dispersive waves; group velocity. Rays and waves: Optical path length. Huygen's and Fermat's principles. Snell's Law and lenses; the focal plane. Geometric optics and principles of the telescope and microscope. Interference and Coherence: Interference with multiple beams. The interference term and fringe visibility. Young's slits experiment. The Michelson and MachZehnder interferometers. Antireflection coatings. The FabryPerot interferometer. Partial coherence and fringe visibility. Coherence time and coherence length. Interference between N equally spaced sources. Diffraction: Introduction to Fresnel diffraction; Fraunhofer diffraction as farfield case. Derivation of Fraunhofer pattern for single slit, discussion of circular aperture. The diffraction grating. Dispersion. Diffraction limits on optical systems. Definition of resolution, Rayleigh criterion and resolving power. Resolving power of the telescope and grating. Lasers: Interaction between light and matter. The Einstein relations. Obtaining and maintaining lasing action. The properties of laser light. 
PH20015: Electronic instrumentation and semiconductor devices 
Credits: 6 
Level: Intermediate 
Semester: 1 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH10008 and take PH10007 and take PH10003 and while taking this unit you must take PH20017 
Aims & Learning Objectives: The aims of this unit are to provide an introduction to the instrumentation techniques typically used in experimental physics and to explore some of the physics underlying the behaviour of electrons in semiconductor materials and the operation of simple semiconductor devices. After taking this unit the student should be able to * recognise the function of the main elements of instrumentation systems * describe the common sources of electronic noise and how one might reduce it * explain the principles of negative feedback as used in measurement systems * design and perform calculations on simple transistor and opamp circuits * discuss the basic concepts of semiconductor physics * calculate carrier concentrations and effective masses * outline the basic principles of semiconductor device operation. Content: Electronic Instrumentation Systems. Impedance loading effects. Introduction to noise and common sources of noise. Signal to noise ratio. Noise in cascaded systems.Detectors and Sensors. Diode detectors. Rectification. Phototransistors, thermistors, transducers, bridge circuits. Linearity, accuracy, sensitivity and dynamic range.Feedback. Principles of negative feedback. Reasons for using it. Gain bandwidth product. Stability of NFB systems. Comparators and the use of positive feedback.Amplification. Operational amplifier based systems. Ideal and real devices. Frequency response. Differential and instrumentation amplifiers. Discrete JFET based systems. Electrical characteristics. Load lines. Large signal and small signal analysis. The use of equivalent circuits. Common source amplifiers. Noise Reduction and Signal Conditioning. Filtering. Active and passive filters. Using feedback to reduce noise. Noise reduction by signal averaging. Commonmode rejection. Lockin detection. Electronic integrators and differentiators. Semiconductor Physics and Devices. Basic properties of semiconductors: electrons and holes and their effective masses; extrinsic and intrinsic semiconductors, donors and acceptors. Electron and hole concentrations, semiconductor statistics.Transport properties: electrical conduction and scattering of electrons and holes in solids, drift velocity, resistivity, diffusion, electronhole recombination, recombination length. The Hall effect.The pn junction: the unbiased pn junction, junction formation, depletion layer width. Biased pn junctions: band profiles, depletion region width, junction capacitance. Balance of drift and diffusion currents, qualitative introduction to the ideal diode equation, reverse bias breakdown.The JFET: electrostatics as a function of gate bias, pinchoff, saturation. Electrical characteristics of nchannel JFET. 
PH20016: Building blocks of the universe 
Credits: 6 
Level: Intermediate 
Semester: 2 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH20013 or take PH20060 
Aims & Learning Objectives: The aims of this unit are to give an overview of our current picture of elementary particles and the forces between them, to describe properties and reactions of atomic nuclei and to discuss how these enable us to understand the origin of the Universe and the elements, stars and galaxies within it. After taking this unit the student should be able to: * describe the classification of fundamental particles and explain terms used in their description; * describe the characteristics of the fundamental forces, and quote and use conservation laws to determine allowed particle reactions; * apply decay laws to problems in particle and nuclear physics, and define and perform simple calculations on cross section and centre of mass frame; * discuss binding in nuclei and explain the energetics and mechanisms of radioactive decay; * describe the liquid drop and shell models of nuclei and use them to calculate and interpret nuclear properties; * describe the physical processes involved in fission and fusion reactions and in stellar nucleosynthesis; * give a qualitative description of the early stages of the Universe and the condensation of particles, nuclei and atoms from the primeval fireball. Content: Decays and Interactions: Particle decay laws, halflife and mean lifetime, generation and decay. Particle kinematics and the discovery of the neutrino. Elementary Particles: Quarks, leptons and mediators. Antiparticles. Hadrons (baryons and mesons) in terms of multiplets. Baryon and lepton number. Fundamental Interactions: The four forces. The exchange particle model and Feynman diagrams. The discovery of the W and Z. Conservation laws. Unification of forces. The Nucleus: Nucleon interactions and binding energy. Nuclear size and mass. Radioactive Decay: Betadecay. Electron and positron emission; Kcapture. Alpha decay : energetics and simplified tunnelling theory. The liquid drop model and semiempirical mass formula. The shell model, nuclear spin, excited states. Nuclear Reactions and Fission: Centre of mass frame. Scattering, spontaneous fission, fission products. Induced fission, chain reactions, delayed neutrons. Nuclear Fusion Reactions: Principles of fusion reactions. The Cosmic Connection: Stellar nucleosynthesis The Big Bang revisited. Separation of unified forces. Inflation theory. Formation of elementary particles. Cosmic nucleosynthesis. Dark matter in the universe. MACHOs, WIMPs and Winos. 
PH20017: Introduction to condensed matter physics 
Credits: 6 
Level: Intermediate 
Semester: 1 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must (take PH10005 or take PH10053) and take PH10007 and take PH10008 (or equivalents). 
Aims & Learning Objectives: The aims of this unit are to introduce students to the basic ideas that underlie solid state physics, with emphasis on the behaviour of electrons in crystalline structures, particularly in materials that are metallic or semiconducting. After taking this unit the student should be able to: * apply knowledge of how crystalline structures vibrate and the associated theories of heat capacity; * discuss why it is that classical theories fail and why electrons in solids have to be treated as quantum mechanical waves; * explain the concept of density of states; * describe how allowed and forbidden energy bands arise as a result of crystal potentials and how the properties of electrons in allowed energy bands determine the electrical and optical behaviour; * appreciate the difference between metals, semiconductors and insulators; * discuss the factors that control the electrical conductivity of metals and semiconductors; * know the ways in which crystal structures are described formally and relate structures in real space to those in reciprocal space; * describe how the diffraction of Xrays and of neutrons is related to the properties of the reciprocal lattice and solve simple problems associated with the determination of crystal structures. Content: Vibrations of crystal structures. Optical and acoustic modes. Phonons. Heat capacity and the failure of classical physics. The Einstein (and possibly the Debye) model. The classical free electron theory and the further failure of classical physics. The quantum free electron theory (electrons as waves). The basic properties of metals; density of states and the Fermi sphere. The effect of crystalline structure on electron behaviour: allowed and forbidden energies from another viewpoint; introduction of momentum (k) space. The distinction between metals, semiconductors and insulators. Energy bands and effective masses; electrons and holes; basic properties of semiconductors; the effects of doping; donors and acceptors; the Hall effect. Basic crystal structures; translational symmetry; space lattices; unit cells; Miller indices. Diffraction of waves in crystalline structures; Bragg law; the reciprocal lattice and Brillouin zones. Xray and neutron diffraction studies of crystal structures. 
PH20018: Programming skills 
Credits: 6 
Level: Intermediate 
Semester: 2 
Assessment: CW60EX40 
Requisites: 
Before taking this unit you must take PH10007 and take PH10008 (or equivalent). 
Aims & Learning Objectives: The aims of this unit are to introduce and develop structured programming skills in a highlevel language as a tool for the numerical solution of physical problems. A further aim is to develop the student's awareness of the sources of error in numerical calculations and the means of reducing them. After taking the unit the student should be able to: * carry out the structured design of a computer program using flowcharts or pseudocode; * give examples of the introduction of rounding errors due to numerical techniques and methods for minimising such problems; * write computer programs in a high level structured language including arithmetic expressions, loops, branching instructions and arrays; * describe methods for testing and debugging programs and apply these techniques to the student's own computer programs; * outline the advantages of using subprograms and write computer programs in a high level structured language using external subprograms; * use numerical techniques to solve simple Physics problems. Content: Introduction to numerical analysis; use of computers in numerical analysis; basic vocabulary of computers; compilation, linking, memory, variable types, generic control structures and loops; conditionals; input and output; arrays; floating point roundoff and truncation errors; maximum integer size; syntax of the C language; intrinsic functions of C; operators and precedence; drives, files and directories in UNIX systems; essential UNIX commands and editing; rootfinding; function evaluation via series expansion and lookup tables; matrix diagonalisation; normal mode problems; subprograms; modules; libraries; pointers; structures in C; inheritances; complex numbers; transfer matrix and shooting methods for simple finite quantum well problems as an example application. 
PH20019: Mathematics for scientists 3 
Credits: 6 
Level: Intermediate 
Semester: 1 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH10008 
Aims & Learning Objectives: The aim of this unit is to introduce mathematical concepts and techniques required by science students, and to show how these may be used for different applications. It also aims to continue the development of students' problemsolving skills and their understanding of mathematical results. After taking this unit the student should be able to: * find the eigenvalues and eigenvectors of matrices and apply these to the diagonalisation of quadratic forms; * calculate the normal modes of coupled vibrational systems; * evaluate Fourier series and Fourier and Laplace transforms, and use their properties to solve problems; * use transform methods to solve differential equations; * apply transform methods in image and signal processing. Content: Eigenvalues and eigenvectors (6 hours): Revision of matrix algebra. Homogeneous linear equations. Eigenvalues and eigenvectors of symmetric matrices and their properties. Linear transformations. Diagonalisation of quadratic forms. Normal modes of vibration of ball and spring systems. Transform methods (18 hours): Periodic functions. Harmonic synthesis. Representation as Fourier series, and Fourier components. Truncated series. Fourier sine and cosine series. Expansion of finite range functions. Applications of Fourier series. Complex form of Fourier series and coefficients. Discrete amplitude spectra. Transition to aperiodic functions: the Fourier transform. Integral definition and properties of the Fourier transform. Use of tables in evaluating transforms. Applications to image processing, solution of differential and integral equations, and to physical systems. Convolution. Causal functions and the Laplace transform. Integral definitions and properties of the Laplace transform. Use of tables in evaluating transforms. Applications. Discrete Fourier transform. Sampling theorem and applications to signal processing. 
PH20020: Mathematics for scientists 4 
Credits: 6 
Level: Intermediate 
Semester: 2 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH10008 and take PH20019 and take PH10006 
(for those taking Introduction to Maxwell's Equations).
Aims & Learning Objectives: The aim of this unit is to introduce mathematical concepts and techniques required by science students, and to show how these may be used for different applications. It also aims to continue the development of students' problemsolving skills and their understanding of mathematical results. After taking this unit the student should be able to: * define and transform between Cartesian, polar, spherical polar and cylindrical polar coordinates, and parameterise and sketch curves, surfaces and volumes within these coordinate systems; * solve equations of motion in Cartesian and polar coordinates; * define scalar, vector and conservative fields; * perform line, surface and volume integrals; * evaluate grad, div, curl and Ñ² in Cartesian, polar, spherical polar and cylindrical polar coordinates, and use and interpret vector integral theorems. Either: * derive and interpret Maxwell's equations and their solution in vacuum. Or: * use the axioms of group theory. Content: Vector analysis (16 hours): Differentiation of vectors. Space curves; parameterisation of curves, tangent vector. Polar coordinates; velocity and acceleration. Introduction to scalar and vector fields. Directional derivative; gradient of a scalar field, Ñ as a vector operator in Cartesian coordinates. Introduction to div and curl in Cartesian coordinates; physical interpretation. Identities involving Ñ; definition of Ñ². Tangential line integrals. Classification of fields; conservative fields, potential functions, path independence of line integrals in conservative fields. Orthogonal curvilinear coordinate systems; Cartesian, spherical polar and cylindrical polar coordinates. Surface and volume integrals. Div and curl; definitions as limits of integrals; explicit forms. Ñ² in spherical and cylindrical polar coordinates. Vector integral theorems; divergence and Stokes theorems, derivation and applications. Green's theorem and applications. EITHER: Introduction to Maxwell's equations (8 hours): Derivation of integral and differential forms of Maxwell's equations and continuity equation. The wave equation in sourcefree vacuum. Plane wave solutions. OR: Introduction to group theory (8 hours): Symmetry. The axioms of group theory. Groups, subgroups and cyclic groups. Isomorphisms and equivalence relations. Permutations. Cayley's Theorem. 
PH20021: Laboratory & information skills 2A 
Credits: 6 
Level: Intermediate 
Semester: 1 
Assessment: PR100 
Requisites: 
Before taking this unit you must take PH10011 and take PH10012 and After taking this module you must take PH20022 
Aims & Learning Objectives: The aims of this unit are to further develop student confidence and competence in experimental laboratory skills, data processing, written presentation skills and the use of scientific computer packages. A further aim is to reinforce elements of units PH10013, PH10014 and PH10015 by providing experimental examples in these areas. While taking this unit the student should be able to: * successfully conduct short experiments, following written guidelines, on various topics relating to physics and analogue electronics; * plan, design and carry out a group project consisting of an experimental investigation; * maintain a scientific log book, recording details of experimental method and results to an appropriate standard; * write detailed scientific reports describing experimental work, displaying an appropriate standard of presentation, style, structure, attention to detail and analysis; * carry out simulations using PSpice of electric circuits incorporating transistors and operational amplifiers; * carry out Fourier analysis of simple aperture functions using Matlab. Content: Students will be introduced to devices, instrumentation and measurement systems as found in a modern research environment. A combination of short benchmark experiments and longer open ended projects will be employed. Students will routinely work in pairs but larger groups of four or give will be the norm in longer projects. Experiments will be drawn from topics encompassing optical physics, xrays, electromagnetism, analogue electronics, instrumentation and ultrasonics. These activities will be underpinned by workshops on writing skills and scientific computer packages. 
PH20022: Laboratory & information skills 2B 
Credits: 6 
Level: Intermediate 
Semester: 2 
Assessment: PR100 
Requisites: 
While taking this unit you must take PH20021 
Aims & Learning Objectives: The aims of this unit are to build on the laboratory and written presentation skills developed in PH20021 and to develop the skills required for preparing and delivering oral presentations. An additional aim is to reinforce elements of unit PH20017 by providing experimental examples in this area. While taking this unit the student should be able to: * successfully conduct short experiments, following written guidelines, on various topics relating to physics and analogue electronics; * plan, design and carry out a group project consisting of an experimental investigation; * maintain a scientific log book, recording details of experimental method and results to an appropriate standard; * write detailed scientific reports describing experimental work, displaying an appropriate standard of presentation, style, structure, attention to detail and analysis; * plan, design and carry out a smallscale investigation into a subject relating to electronics instrumentation; * prepare and deliver an oral presentation based on the group physics project and answer questions relating to the presentation. Content: Students will be introduced to devices, instrumentation and measurement systems as found in a modern research environment. A combination of short benchmark experiments and longer open ended projects will be employed. Students will routinely work in pairs but larger groups of four or give will be the norm in longer projects. Experiments will be drawn from topics encompassing optical physics, xrays, electromagnetism, analogue electronics and ultrasonics. These activities will be underpinned by a workshop on oral presentation skills. 
PH20040: B.Sc. placement 
Credits: 60 
Level: Intermediate 
Academic Year 
Assessment: OT100 
Requisites: 
Aims & Learning Objectives: The aims of this unit are for BSc students to undertake a technical work programme within physics or a related discipline, whilst placed at an approved laboratory or other organisation, and to develop transferable, personal and interpersonal skills, relevant to a graduate physicist. On completion of the placement year, the student should have demonstrated: * the ability to apply knowledge and skills gained at the university to a technical work programme in a professional context; * good personal skills in planning and time management, problem solving, decision making and team membership; * good oral communication and presentation skills, including making an oral presentation at the placement conference on the work being carried out; * sound record keeping and report writing skills, including writing a report on the work carried out during the placement and the context of this work in terms of the organisation's overall strategy. Content: The content varies from placement to placement. In choosing the placement, the university will try to ensure that the work programme offers adequate opportunities for the student to demonstrate competence in the following categories: Self management and development, Managing tasks, Communicating clearly and effectively, Working with and relating to others, Applying knowledge and Applying initiative in work problems. 
PH20042: BSc year abroad 
Credits: 60 
Level: Intermediate 
Academic Year 
Assessment: OT100 
Requisites: 
Aims & Learning Objectives: The aims of this unit are for students to gain experience of living and studying in a University outside the UK and to develop the appropriate personal and linguistic skills, in addition to developing their knowledge and understanding of physics and mathematics. While taking this unit, the student should: * develop personal and interpersonal communication skills and the ability to work and interact effectively in a group environment in which cultural norms and ways of operating may be very different from those previously familiar; * develop the selfconfidence and maturity to operate effectively with people from a different cultural background; * develop an understanding of the stresses that occur in working in a different culture from the UK, and learn to cope with those stresses; * in the case of students attending Universities in countries whose language is not English, improve their knowledge of the host language by attending classes therein; * in the case of students attending lectures in a language other than English, develop the ability to operate at a high scientific level in the language of the country concerned; this would include oral communication and comprehension as well as reading and writing. Content: It is assumed that the student abroad will accomplish work equivalent to 60 University of Bath credits (10 units). Details of these are necessarily left to negotiation with individual University, students and the Bath Director of Studies but a sample study programme would include work in Physics, Maths and in Science areas outside these. It would also be appropriate to include Management, work in Language if appropriate, and one or two units in areas more related to the culture of the country in which the student is working. 
PH20059: Relativity & astrophysics [WL] 
Credits: 6 
Level: Intermediate 
Semester: 2 
Assessment: CW20PR13EX67 
Requisites: 
In taking this unit you cannot take PH10004 and before taking this unit you must take PH20060 and while taking this unit you must take PH20061 
Aims: The aims of this unit are
to introduce the concepts and results of special relativity and to provide
a broad introduction to astronomy and astrophysics. An additional aim is
that the student's appreciation of important physical phenomena such as
gravitation and blackbody radiation should be reinforced through their study
in astrophysical contexts. A final aim is to further develop students confidence
and competence in experimental laboratory skills, data processing and written
presentation skills. Learning Outcomes: After taking this unit, the student should be able to: * write down the essential results and formulae of special relativity; * describe the important special relativity experiments (real or thought); * solve simple kinematic and dynamical special relativity problems; * give a qualitative account of how the sun and planets were formed; * describe how stars of differing masses evolve; * give a simple description of the expanding Universe and its largescale structure; * solve simple problems concerning orbital motion, blackbody radiation, cosmological redshift, stellar luminosity and magnitude; * successfully conduct short experiments, following written guidelines, on various topics relating to physics; * write a detailed scientific report describing experimental work, displaying an appropriate standard of presentation, style, structure, attention to detail and analysis. Skills: As PH10004 in regard to lectured content and PH20021 in regard to practical skills. Content: Special Relativity: Galilean transformation. Speed of light  MichelsonMorley experiment; Einstein's postulates. Simultaneity; time dilation; space contraction; invariant intervals; rest frames; proper time; proper length. Lorentz transformation. Relativistic momentum, force, energy. Doppler effect. Astrophysical Techniques: Telescopes and detectors. Invisible astronomy : Xrays,gammarays, infrared and radio astronomy. Gravitation: Gravitational force and potential energy. Weight and mass. Circular orbits; Kepler's Laws; planetary motion. Escape velocity. Solar System: EarthMoon system. Terrestrial planets; Jovian planets. Planetary atmospheres. Comets and meteoroids. Formation of the solar system. The interstellar medium and star birth. Stellar distances, magnitudes, luminosities;blackbody radiation; stellar classification; HertzsprungRussell diagram. Stellar Evolution: Star death: white dwarfs, neutron stars. General Relativity: Gravity and geometry. The principle of equivalence. Deflection of light; curvature of space. Gravitational time dilation. Red shift. Black holes.Large scale structure of the Universe. Galaxies: Galactic structure; classification of galaxies. Formation and evolution of galaxies. Hubble's Law. The expanding universe. The hot Big Bang. Cosmic background radiation and ripples therein. Laboratory: 6x 3 hr laboratory sessions. 
PH20060: Quantum & atomic physics [WL] 
Credits: 6 
Level: Intermediate 
Semester: 1 
Assessment: CW20PR13EX67 
Requisites: 
Before taking this unit you must (take PH10001 or take PH10048) and take PH10008 and while taking this unit you must take PH20063 and in taking this unit you cannot take PH20013 
Aims: The aims of this module
are to introduce the Schrödinger wave equation and its solution in one and
three dimensions, and to explore the interactions responsible for the electronic
structure and spectra of atoms. In the laboratory section of the unit the
aims are the further development of practical and recordkeeping skills,
and the performance of experimental work which supports the lecture material.
Learning Outcomes: After taking this unit the student should be able to: * explain the significance of the wavefunction in determining the physical behaviour of electrons; * show how quantisation arises from boundary conditions; * calculate energy levels in simple model systems; * outline the quantum mechanical description of the hydrogen atom; * discuss the energy levels, angular momenta and spectra of simple atoms, taking into account screening, magnetic interactions and the exchange interaction; * make simple quantitative estimates of magnetic energies in atoms; * use empirical rules to establish the ground state terms and configurations of atoms; * conduct short experiments on various topics, and record details of experimental method and results to an appropriate standard. Skills: As PH20013. Content: Basic assumptions of quantum mechanics: wave functions and probability density. Observables; position, momentum and energy. Schrödinger's equation: time dependence of the wave function. Timeindependent Schrödinger equation and stationary states. Motion in one dimension: the infinite square well; bound state energies and wave functions. Parity of solutions. Motion of free particles. Reflection and transmission at a potential step. Bound states of a finite square well. Tunnelling through a barrier. The harmonic oscillator. Motion in three dimensions: central potentials. Angular dependence of solutions. Angular momentum quantum numbers; s, p and d states. Spin angular momentum. Vector model of the atom. Orbital and spin magnetic moments and their coupling in a oneelectron atom. Fine structure in hydrogen. Factors affecting intensity of spectral lines. Effect of the nuclear magnetic moment on atomic spectra: hyperfine structure, nuclear magnetic resonance. Atoms with more than one electron: Pauli exclusion principle and shell structure. Electronelectron interactions: screening and exchange interaction. Chemical bonding. Nomenclature for labelling atomic configurations and terms. Hund's rules. Fine structure and Zeeman effect in manyelectron atoms. Factors affecting width of spectral lines and introduction to highresolution spectroscopy. Practical laboratory: Performance of experiments designed further to develop practical skills and support lecture material. 
PH20061: Electromagnetic waves & optics [WL] 
Credits: 6 
Level: Intermediate 
Semester: 2 
Assessment: CW20PR13EX67 
Requisites: 
Before taking this unit you must (take PH10005 or take PH10053) and take PH10008 and take PH20060 and in taking this unit you cannot take PH20014 
Aims: The aims of this unit are
to introduce the properties of electromagnetic plane waves, to provide a
mathematical framework for the understanding of the wave nature of light
and to describe the properties of simple optical devices. In the laboratory
section of the unit the aims are the further development of practical and
recordkeeping skills, and the performance of experimental work which supports
the lecture material. Learning Outcomes: After taking this unit the student should be able to: * list the distinguishing features of electromagnetic plane waves and write down a mathematical expression for a linearly or circularly polarised light wave; * construct ray diagrams for use in solving simple geometrical optics problems; * discuss the concept of coherence with regard to the physical properties of the source and the effect of partial coherence on fringe visibility; * derive mathematical expressions for simple diffraction patterns and relate the limits imposed by diffraction to the performance of optical instruments; * outline the mathematical analysis of multiplebeam interference and hence interpret the output from a FabryPérot interferometer; * describe how lasing action is obtained and maintained and outline the main properties of laser light; * conduct short experiments on various topics, and record details of experimental method and results to an appropriate standard. Skills: as PH20014. Content: Electromagnetic plane waves: The em spectrum; sources and production of light; wave and photon description; the optical region; Revision of 1D waves. 3D plane waves, vector nature of em waves; relationships between E B and k. Polarisation. Methods of obtaining linearly polarised light, Law of Malus. Circular and elliptical polarisation. Energy and the Poynting vector. Impedance. Phase velocity, permittivity, permeability. Refractive index and its microscopic origin. Concept of birefringence. Dispersive waves; group velocity. Rays and waves: Optical path length. Huygen's and Fermat's principles. Snell's Law and lenses; the focal plane. Geometric optics and principles of the telescope and microscope. Interference and Coherence: Interference with multiple beams. The interference term and fringe visibility. Young's slits experiment. The Michelson and MachZehnder interferometers. Antireflection coatings. The FabryPerot interferometer. Partial coherence and fringe visibility. Coherence time and coherence length. Interference between N equally spaced sources. Diffraction: Introduction to Fresnel diffraction; Fraunhofer diffraction as farfield case. Derivation of Fraunhofer pattern for single slit, discussion of circular aperture. The diffraction grating. Dispersion. Diffraction limits on optical systems. Definition of resolution, Rayleigh criterion and resolving power. Resolving power of the telescope and grating. Lasers: Interaction between light and matter. The Einstein relations. Obtaining and maintaining lasing action. The properties of laser light. Practical laboratory: Performance of experiments designed further to develop practical skills and support lecture material. 
PH20062: Building blocks of the universe [WL] 
Credits: 6 
Level: Intermediate 
Semester: 2 
Assessment: CW20PR13EX67 
Requisites: 
Before taking this unit you must take PH20013 or take PH20060 and in taking this unit you cannot take PH20016 
Aims: The aims of this unit are
to give an overview of our current picture of elementary particles and the
forces between them, to describe properties and reactions of atomic nuclei
and to discuss how these enable us to understand the origin of the Universe
and the elements, stars and galaxies within it. In the laboratory section
of the unit the aims are the further development of practical and reportwriting
skills, and the performance of experimental work which supports the lecture
material. Learning Outcomes: After taking this unit the student should be able to: * describe the classification of fundamental particles and explain terms used in their description; * describe the characteristics of the fundamental forces, and quote and use conservation laws to determine allowed particle reactions; * apply decay laws to problems in particle and nuclear physics, and define and perform simple calculations on cross section and centre of mass frame; * discuss binding in nuclei and explain the energetics and mechanisms of radioactive decay; * describe the liquid drop and shell models of nuclei and use them to calculate and interpret nuclear properties; * describe the physical processes involved in fission and fusion reactions and in stellar nucleosynthesis; * give a qualitative description of the early stages of the Universe and the condensation of particles, nuclei and atoms from the primeval fireball; * conduct short experiments on various topics, record details of experimental method and results to an appropriate standard, and write a detailed scientific report displaying an appropriate standard of presentation, style, structure, attention to detail and analysis. Skills: As PH20016. Content: Decays and Interactions: Particle decay laws, halflife and mean lifetime,generation and decay. Particle kinematics and the discovery of the neutrino. Elementary Particles: Quarks, leptons and mediators. Antiparticles. Hadrons (baryons and mesons) in terms of multiplets. Baryon and lepton number. Fundamental Interactions: The four forces. The exchange particle model and Feynman diagrams. The discovery of the W and Z. Conservation laws. Unification of forces. The Nucleus: Nucleon interactions and binding energy. Nuclear size and mass. Radioactive Decay: Betadecay. Electron and positron emission; Kcapture.Alpha decay : energetics and simplified tunnelling theory. The liquid drop model and semiempirical mass formula. The shell model, nuclear spin, excited states. Nuclear Reactions and Fission: Centre of mass frame. Scattering, spontaneous fission, fission products. Induced fission, chain reactions, delayed neutrons. Nuclear Fusion Reactions: Principles of fusion reactions. The Cosmic Connection: Stellar nucleosynthesis The Big Bang revisited. Separation of unified forces. Inflation theory. Formation of elementary particles. Cosmic nucleosynthesis. Dark matter in the universe. MACHOs, WIMPs and Winos. Practical laboratory: Performance of experiments designed further to develop practical skills and to support lecture material. 
PH20063: Introduction to condensed matter physics [WL] 
Credits: 6 
Level: Intermediate 
Semester: 1 
Assessment: CW20PR13EX67 
Requisites: 
Before taking this unit you must (take PH10005 or take PH10053) and take PH10007 and take PH10008 and in taking this unit you cannot take PH20017 
Aims: The aims of this unit are
to introduce students to the basic ideas that underlie solid state physics,
with emphasis on the behaviour of electrons in crystalline structures, particularly
in materials that are metallic or semiconducting. In the laboratory section
of the unit the aims are the further development of practical and reportwriting
skills, and the performance of experimental work which supports the lecture
material. Learning Outcomes: After taking this unit the student should be able to : * apply knowledge of how crystalline structures vibrate and the associated theories of heat capacity; * discuss why it is that classical theories fail and why electrons in solids have to be treated as quantum mechanical waves; * explain the concept of density of states; * describe how allowed and forbidden energy bands arise as a result of crystal potentials and how the properties of electrons in allowed energy bands determine the electrical and optical behaviour; * appreciate the difference between metals, semiconductors and insulators; * discuss the factors that control the electrical conductivity of metals and semiconductors; * know the ways in which crystal structures are described formally and relate structures in real space to those in reciprocal space; * describe how the diffraction of Xrays and of neutrons is related to the properties of the reciprocal lattice and solve simple problems associated with the determination of crystal structures; * conduct short experiments on various topics, record details of experimental method and results to an appropriate standard, and write a skeleton scientific report displaying an appropriate standard of structure, attention to detail and analysis. Skills: As PH20017. Content: Vibrations of crystal structures. Optical and acoustic modes. Phonons. Heat capacity and the failure of classical physics. The Einstein (and possibly the Debye) model. The classical free electron theory and the further failure of classical physics. The quantum free electron theory (electrons as waves). The basic properties of metals; density of states and the Fermi sphere. The effect of crystalline structure on electron behaviour: allowed and forbidden energies from another viewpoint; introduction of momentum (k) space. The distinction between metals, semiconductors and insulators. Energy bands and effective masses; electrons and holes; basic properties of semiconductors; the effects of doping; donors and acceptors; the Hall effect. Basic crystal structures; translational symmetry; space lattices; unit cells; Miller indices. Diffraction of waves in crystalline structures; Bragg law; the reciprocal lattice and Brillouin zones. Xray and neutron diffraction studies of crystal structures. Practical laboratory: Performance of experiments designed further to develop practical skills and support lecture material. 
PH30023: Electromagnetism 
Credits: 6 
Level: Honours 
Semester: 1 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH20014 and take PH20020 
Aims & Learning Objectives: The aims of this unit are develop a full formal vectorial description of electric, magnetic and electromagnetic fields in infinite materials and at boundaries between materials, to derive some individual solutions and to make use of them in a few important applications. After taking this unit the student should be able to: * manipulate full vectorial versions of Maxwell's equations in static and timevarying cases; * analyse in detail the propagation of vectorial plane waves in vacuum and in various materials (e.g. lossy dielectrics, metals and plasmas); * describe the origins of polarisation and magnetisation in materials; * match electric and magnetic fields at boundaries between materials and explain the origins of Brewster's angle, total internal reflection and tunnelling; * calculate the energy density in static and timevarying fields; * calculate and make use of the electromagnetic Poynting vector; * use static and timevarying scalar and vector potentials to calculate electric, magnetic and electromagnetic fields; * outline the basic features of electric and magnetic dipoles; * analyse the modes of rectangular metallic waveguides (cutoff, total number of modes, impedance, power flow); * describe some simple antennas and analyse their basic characteristics using magnetic vector potentials. Content: Mathematical review: vector calculus; div, grad, curl; divergence and Stoke's theorem. Maxwell's equations: Differential form of "static" Maxwell equations from Gauss, BiotSavart and Ampere Laws. Time variations; Faraday's Law, the continuity equation and vacuum displacement current. Solutions in infinite vacuum: The wave equation. Plane wave solutions and properties; polarisation, impedance. Electromagnetic energy. Poynting's theorem. Radiation pressure. Solutions in infinite materials: Concepts of linearity, isotropy and homogeneity. Characterisation of materials in terms of macroscopic parameters. Multipole expansion of electrostatic fields. Dipoles, susceptibility and polarisation / magnetisation. Capacitors. The modified wave equation; solution in conductors, dielectrics, lossy media and plasma. Boundaries between media: The general electromagnetic boundary conditions. Plane waves at a planar boundary; general angle of incidence (Fresnel equations). Brewster and critical angles. Coefficients of transmission and reflection at normal incidence. Radiation: Electromagnetic potentials; retarded potentials; near and far fields; radiation from a Hertz dipole; simple antennas and antenna arrays. Guided waves: The rectangular metal pipe waveguide. 
PH30024: Contemporary physics 
Credits: 6 
Level: Honours 
Semester: 1 
Assessment: ES100 
Requisites: 
Students should have taken an appropriate selection
of Year 1 and Year 2 Physics units in order to undertake this unit. Aims & Learning Objectives: The aim of this unit is to enable students to find out about some of the most exciting developments in contemporary Physics research. While taking this unit the student should be able to: * demonstrate good time management skills in allocating appropriate amounts of time for the planning, research and writing of reports; * carry out literature searching methods for academic journals and computerbased resources in order to research the topics studied; * develop the ability to extract and assimilate relevant information from extensive sources of information; * develop structured report writing skills; * write a concise report following each seminar, at a level understandable by a final year undergraduate unfamiliar with the subject of the seminar; * write a detailed technical report on one of the seminar subjects of the student's choice, displaying an appropriate level of technical content, style and structure. Content: This unit will be based around 4 seminars from internal and external speakers who will introduce topics of current interest in Physics. Students will write a short report following each seminar and then choose one of these subjects on which to research and write a longer technical report. Topics are likely to include recent developments in: Astrophysics and Cosmology; Particle Physics; Medical Physics; Laser Physics; Semiconductor Physics; Superconductivity; Quantum Mechanical Simulation of Matter; 
PH30025: Equations of science 
Credits: 6 
Level: Honours 
Semester: 2 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH10007 and take PH10008 and take PH20019 and take PH20020 
Aims & Learning Objectives: The aims of this unit are to introduce concepts and methods used in solving some of the most important equations, both linear and nonlinear, which arise in the natural sciences, and to introduce students to a broad range of examples and applications. After taking this unit the student should be able to: * distinguish linear and nonlinear equations and contrast the different forms of solution which arise; * recognise some of the key equations which arise in the natural sciences; * apply the separation of variables method to linear partial differential equations, and solve the resulting ordinary differential equations by series solution; * use superposition methods for inhomogeneous equations; * determine solutions to some of the key nonlinear equations, and analyse nonlinear ordinary differential equations; * analyse onedimensional difference equations. Content: Linear equations of science (12 hours): Derivation of the diffusion equation as an example of how partial differential equations arise in the natural sciences. Introduction to Laplace's equation, Poisson's equation, wave equation, Schrodinger's equation. Linearity and superposition. Boundary conditions. Solution by separation of variables; examples showing separation in Cartesian, cylindrical and spherical coordinate systems. Series solutions of differential equations; examples including Legendre polynomials, spherical harmonics and Bessel functions. Solution of inhomogeneous ODE's. Examples from the natural sciences. Nonlinearity and chaos (12 hours): Examples of nonlinearity in the natural sciences; Nonlinear wave equations, solitary waves, physical examples. Nonlinear differential equations: phase space, trajectories, fixed points, bifurcation. Examples from the natural sciences. Nonlinear difference equations: orbits, cobwebs, fixed points, bifurcations, chaos. Examples from the natural sciences. 
PH30027: Signals processing 
Credits: 6 
Level: Honours 
Semester: 1 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH10003 and take PH20019 
Aims & Learning Objectives: The aims of this course are to introduce the basic concepts of analogue and digital signal processing and apply them to a range of examples. After taking this unit the student should be able to: * identify common noise sources and estimate their values in a given experiment; * understand system responses, Laplace transforms, Ztransforms and transfer functions; * understand the basics of digital and analogue signal processing; * design digital and analogue filters with a desired frequency response; * design and develop mathematical models for feedback systems and explain their advantages for measurement and control. * apply signal processing techniques to a variety of electromechanical systems. Content: Noise and random signals. Noise sources. AC measuring techniques and signal recovery methods. The Laplace transform and analogue signal processing, analogue filters. Sampled signals and the sampling theorem. Introduction to digital signal processing, z transform. Frequency response. Design of digital filters using z and Fourier transforms. Feedback, and its application to measurement and control systems. Static and dynamic theory of feedback. Modelling of physical systems. Case studies in the applications of analogue and digital signal analysis. Examples chosen from, for example, vibrating systems, fluid dynamics, speech recognition and synthesis, and image processing. 
PH30028: Real solids, surfaces & soft matter physics 
Credits: 6 
Level: Honours 
Semester: 1 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH20017 and take PH20019 and take PH20020 
Aims & Learning Objectives: The aims of this unit are to introduce areas of condensed matter physics that extend beyond the conventional domain of regular, infinite, crystalline solids. After taking this unit the student should be able to: * relate the electronic, optical and mechanical properties of real crystals to their defects; * make quantitative estimates of the parameters that govern the behaviour of real solids; * describe the structure and properties of amorphous solids; * explain the basic features of the observed crystal and electronic structure of clean surfaces; * sketch surface unit meshes and reciprocal nets and write down the associated Wood notation; * describe, compare and contrast experimental probes of surfaces and soft condensed matter; * describe the structure of polymers, colloids and surfactants and how these impact upon their properties. Content: Real Solids (8 lectures). Defects in crystals: point defects and dislocations in crystals. Effect on electronic, optical and mechanical properties. Point defects in thermal equilibrium. Self diffusion. Ionic conductivity. Colour centres. Dislocations: slip, shear strength; edge and screw dislocations. Dislocation loops and networks. Introduction to amorphous solids. Topological disorder. Determination of glass structure. Short range order, vibrational states and thermal conductivity of glasses. Surface physics (8 lectures): importance of surfaces, eg catalysis, corrosion, epitaxial growth. Clean and real surfaces. Surface energy. Surface crystal structure; relaxation and reconstruction; Wood notation. Surface electronic structure; the work function, 2band model of surface states; adsorbates. Experimental probes of atomic and electronic structure; electron spectroscopies, low energy electron diffraction, scanning tunnelling microscopy. Soft Condensed Matter (8 lectures). Polymers: Chemical structure; Models for the conformation of polymers: the random walk, large N limit, freely jointed chains, Gaussian chains. Polymer solutions and melts. Colloids: Colloid structure, Brownian motion, sedimentation. Interacting colloid particles, phase behaviour, crystals and glasses. Surfactants: self assembly, Micelle formation, shapes of surfactant assemblies. Slow dynamics and the Glass transition. Experimental techniques: Static and dynamic light scattering; xray and neutron scattering. 
PH30029: Thermodynamics & statistical mechanics 
Credits: 6 
Level: Honours 
Semester: 2 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH10002 and take PH10008 (or equivalent). 
Aims & Learning Objectives: The aims of this unit are to develop an appreciation of the concepts of classical thermodynamics and their application to physical processes and to introduce the concepts of statistical mechanics, showing how one builds from an elementary treatment based on ways of arranging objects to a discussion of Fermi and Bose systems. After taking this unit, the student should be able to: * define terms such as isobaric, isothermal, adiabatic and state and apply the 1st and 2nd laws; * calculate work done and heat interchanges as various paths are followed on a pV diagram; * explain the operation of, and carry out calculations for, heat engines and refrigerators; * write down the Clausius Clapeyron equation and describe its applications; * carry out simple calculations on various Virial equations of state; * solve problems using Maxwell's relations in various contexts; * define entropy, temperature, chemical potential in statistical terms; * derive the FermiDirac, BoseEinstein, Boltzmann and Planck distribution functions and apply them to simple model systems; * appreciate when the quantum mechanical and classical approaches should be used. Content: Classical thermodynamics: Zeroth law and thermal equilibrium. Temperature scales. Thermodynamic equilibrium. Equations and functions of state. Concept of reversibility. First law, isothermal and adiabatic processes, work done. Second law, heat engines, refrigerators, the Carnot cycle, efficiency and entropy. Thermodynamic potentials, Maxwell's relations and their applications. Open systems, the chemical potential, GibbsDuhem relation, equilibrium between phases and the ClausiusClapeyron equation. First and second order phase changes and Ehrenfest's equations. Third law. Statistical Mechanics: Probability theory and statistical weight (degeneracy). Ensemble and ensemble averages. Microcanonical ensemble and the basic postulate. Systems in thermal contact and thermal equilibrium. Statistical definitions of temperature, entropy and chemical potential. Canonical ensemble, Boltzmann factor and partition function illustrated by harmonic oscillator and twostate system. Third law of thermodynamics. Grand canonical ensemble, Gibbs factor and partition function illustrated by density fluctuations at the critical point. Perfect gases  density of states, bosons, fermions and the grand partition function. Average occupancy of a state. FermiDirac and BoseEinstein distribution functions and their classical limit. Properties of Fermi systems: ground state of a Fermi gas, density of states, Fermi gas at nonzero temperature, electrons in solids, model of a neutron star. Properties of Bose systems: BoseEinstein condensation, superfluidity, Planck distribution function and StefanBoltzmann law of radiation. Properties of classical perfect gases and conditions of validity for the classical regime. Classical perfect gas of molecules, Maxwell speed distribution function. Debye versus Einstein models of a solid. Application of statistical mechanics to classical and quantum systems. 
PH30030: Quantum mechanics 
Credits: 6 
Level: Honours 
Semester: 2 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH10007 and take PH10008 and take PH20019 and take PH20020. Alevel Physics is desirable in order to undertake this unit. 
Aims & Learning Objectives: The aims of this unit are to show how a mathematical model of considerable elegance may be constructed, from a few basic postulates, to describe the seemingly contradictory behaviour of the physical universe and to provide useful information on a wide range of physical problems. After taking this unit the student should be able to: * explain the relation between wave functions, operators and experimental observables; * justify the need for probability distributions to describe physical phenomena; * set up the Schrödinger equation for simple model systems; * derive eigenstates of energy, momentum and angular momentum; * apply approximate methods to more complex systems. Content: Quantum mechanical concepts and models: The "state" of a quantum mechanical system. Hilbert space. Observables and operators. Eigenvalues and eigenfunctions. Dirac bra and ket vectors. Basis functions and representations. Probability distributions and expectation values of observables. Schrödinger's equation: Operators for position, time, momentum and energy. Derivation of timedependent Schrodinger equation. Correspondence to classical mechanics. Commutation relations and the Uncertainty Principle. Time evolution of states. Stationary states and the timeindependent Schrödinger equation. Motion in one dimension: Free particles. Wave packets and momentum probability density. Time dependence of wave packets. Bound states in square wells. Parity. Reflection and transmission at a step. Tunnelling through a barrier. Linear harmonic oscillator. Motion in three dimensions: Stationary states of free particles. Central potentials; quantisation of angular momentum. The radial equation. Square well; ground state of the deuteron. Electrons in atoms; the hydrogen atom. Hydrogenlike atoms; the Periodic Table. Spin angular momentum: Pauli spin matrices. Identical particles. Symmetry relations for bosons and fermions. Pauli's exclusion principle. Approximate methods for stationary states: Time independent perturbation theory. The variational method. Scattering of particles; the Born approximation. 
PH30031: Simulation techniques 
Credits: 6 
Level: Honours 
Semester: 1 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH20020 
Aims & Learning Objectives: The aims of this unit are to identify some of the issues involved in constructing mathematical models of physical processes, and to introduce major techniques of computational science used to find approximate solutions to such models. After taking this unit the student should be able to: * dedimensionalise an equation representing a physical system; * discretise a differential equation using grid and basis set methods; * outline the essential features of each of the simulation techniques introduced; * give examples of the use of the techniques in contemporary science; * use the simulation schemes to solve simple examples by hand; * describe and compare algorithms used for key processes common to many computational schemes. Content: Construction of a mathematical model of a physical system; dedimensionalisation, order of magnitude estimate of relative sizes of terms. Importance of boundary conditions. The need for computed solutions. Discretisation using grids or basis sets. Discretisation errors. The finite difference method; review of ODE solutions. Construction of difference equations from PDEs. Boundary conditions. Applications. The finite element method; Illustration of global, variational approach to solution of PDEs. Segmentation. Boundary conditions. Applications. Molecular Dynamics and MonteCarlo Methods; examples of Nbody problems, ensembles and averaging. The basic MD strategy. The basic MC strategy; random number generation and importance sampling. Applications in statistical mechanics. Simulated annealing. Computer experiments. Solving finite difference problems via random walks. Other major algorithms of computational science; the Fast Fourier Transform, matrix methods, including diagonalisation, optimisation methods, including nonlinear least squares fitting. 
PH30032: Lasers & modern optics 
Credits: 6 
Level: Honours 
Semester: 2 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH20013 and take PH20017 and take PH30023 
Aims & Learning Objectives: The aim of this unit is to provide a treatment of the interactions of light with matter, with particular emphasis on the generation and manipulation of laser radiation in modern optical systems. After taking this unit the student should be able to: * analyse the diffraction of beams, in particular the propagation of Gaussian beams; * design simple resonant cavities and analyse their main features; * apply matrix methods to paraxial rays in multielement systems of lenses and mirrors; * describe and analyse the interactions between light and matter that lead to spontaneous emission and lasing in 3 and 4level systems; * treat cw, modelocked and Qswitched laser operation and describe the resulting temporal, spectral and power characteristics; * use the index ellipsoid to analyse the changing polarisation state of light in birefringent materials and to design simple half and quarterwave plates; * describe the basic features of guided modes in planar and fibre waveguides and outline basic fabrication techniques; * describe the origins of second and third order optical nonlinearities and analyse their effects on laser light in simple cases; * treat the effects of group velocity dispersion and selfphase modulation on short pulses, and outline briefly how solitons form in optical fibres; * discuss and analyse the operation of simple electooptic modulators. Content: Diffractive Optics: Bandwidth of a finite pulse, diffraction at apertures, birefringence, matrix methods, Gaussian beams, laser cavities and resonators. Lasers: Principles of laser operation, temporal and spectral characteristics, types of lasers, linewidths and broadening, Q switching and mode locking. Manipulation of light: Dielectric waveguides, optical fibres, dispersion of short pulses, second and third order nonlinear optics, electrooptic modulation, solitons. 
PH30033: Lowdimensional semiconductors 
Credits: 6 
Level: Honours 
Semester: 2 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH20013 and take PH20015 and take PH20017 and take PH30023 
Aims & Learning Objectives: The aims of this unit are to give an introduction to the semiconductor physics relating to a range of advanced electronic and optoelectronic devices and to develop an understanding of how fundamental principles affect device performance. After taking this unit the student should be able to: * explain the concept of bandgap engineering and draw energy band diagrams of undoped and doped semiconductor heterostructures; * discuss the main properties of semiconductor quantum wells, superlattices and quantum dots and their uses in electronic and optoelectronic devices; * outline the origin of tunnelling and resonant tunnelling and explain the operation of the resonant tunnelling diode; * describe the interactions between electrons and photons such as absorption, spontaneous emission and stimulated emission; * give examples of common optoelectronic devices for emitting, detecting and modulating light, and explain their physical principles of operation; * distinguish between the optoelectronic properties of bulk and quantum well semiconductors. Content: Semiconductor heterostructures: Alloys, Vegard's law, bandgap engineering, band offsets. Semiconductor quantum wells: energy levels, density of states, occupation of subbands. Superlattices, tunnelling barriers, resonant tunnelling. Quantum wires and quantum dots. Strained systems: atomic structure, critical interface, effects of strain on bulk bandstructures. Electronic properties and devices: Tunnelling barriers, transmission coefficient, current and conductance. Resonant tunnelling, resonant tunnelling diode. Doped heterostructure: band bending at interfaces, modulation doping, construction of band diagrams, MODFET. Optoelectronic properties and devices: Electronphoton interaction in semiconductors. Optical absorption in bulk semiconductors: spectral dependence, photocurrent, PIN photodiodes, avalanche detectors, solar cells. Optical absorption in quantum wells: interband and intersubband transitions, selection rules. Excitons in bulk semiconductors and quantum wells. Quantumconfined Stark effect and quantum well modulators. Optical emission in semiconductors: radiative and nonradiative transitions, lightemitting diodes, optical gain in bulk and quantum well semiconductors, semiconductor optical amplifiers, bulk and quantum well semiconductor lasers. Advanced semiconductor lasers: distributed feedback lasers, vertical cavity surface emitting lasers, quantum cascade lasers. 
PH30034: Superconductivity & magnetism 
Credits: 6 
Level: Honours 
Semester: 2 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH10006 and take PH20017 and take PH20013 
Aims & Learning Objectives: The aim of this unit is to explain the basic properties of superconductivity and magnetism, and illustrate contemporary applications of these phenomena. After taking this unit the student should be able to: * describe the basic properties of superconductors; * apply fundamental knowledge of superconductors to applications of superconductivity in technology and the research laboratory; * demonstrate a basic understanding of the origin and types of magnetic order; * describe and explain the origins of magnetic microstructure; * explain the magnetisation process and hysteresis; * describe magnetooptical effects and how magnetism impacts upon transport properties; * make quantitative estimates of the parameters that govern superconductivity and magnetism. Content: Superconductivity (12 lectures): basic phenomenology: critical temperature, zero resistance, critical magnetic field, Meissner effect, penetration depth, coherence length, superfluidity. Two fluid model. GinsburgLandau theory. Microscopic theory, Cooper pairs, electron phonon interaction, isotope effect, BCS model and the energy gap. Type I and type II superconductors, vortex states. Applications of type II materials. Tunnelling in superconductors, the Josephson effect, SQUIDS. High Tc superconductivity. Other nonconventional superconductors. Magnetism: (12 lectures): Microscopic origins of magnetism; magnetic ordering: para, ferro, antiferro and ferri magnetism; itinerant magnetism; the exchange interaction; Heisenberg model; demagnetising fields and crystalline anisotropy; domains and magnetic microstructure; MH hysteresis curves, coercivity, soft and hard magnetic materials; dynamic effects (ferromagnetic resonance, spin waves); thin film magnetism; magnetooptical phenomena: Kerr effect and applications; magnetoelectronics and spintronics: spin valves, GMR, applications. Contemporary applications of magnetism. 
PH30035: Medical physics 
Credits: 6 
Level: Honours 
Semester: 2 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH10008 and take PH20014 and take PH20016 
Aims & Learning Objectives: The aims of this unit are to introduce the application of physics to medicine in the specific areas of medical imaging and ionising radiation and to show how core physics from earlier modules can be applied to these medical applications. After taking this unit the student should be able to: * describe the physical principles underlying specific areas of medical imaging and ionising radiation therapy; * perform basic calculations on medical ultrasound, ionising radiations and magnetic resonance imaging. Content: This unit is under development in 2004/5; not all of the sections listed below will necessarily be covered. Introduction: Introduction to medical physics and imaging. Physical properties of body tissues. Safety aspects. Ultrasonic Imaging: Generation and structure of ultrasonic fields; Piezoelectric devices. Nearfield and far field of transducers, focused fields and pulsed fields. Arrays. Field measurements. Nonlinear propagation. Attenuation and absorption: Characteristics of typical propagation media and effects on system design.Plane wave reflection and transmission at interfaces. Scattering from discrete scatterers. Introduction to scattering from random media. Limitations on resolution of systems. Doppler Ultrasound: The Doppler principle. Continuous wave and pulsed Doppler instruments. Medical ultrasound systems in current use and clinical applications. Exposure measurement and safety. Ionising radiation: Photon, electron and heavier particle absorption and scattering processes in tissue, including the effects of incident energy and tissue inhomogeneity. Influence of above processes on radiotherapeutic and radiodiagnostic techniques and equipment. Principles of dosimetry. Magnetic Resonance Imaging: Production of crosssectional images of tissue properties, and function, using nuclear magnetic resonance imaging. Spatial resolution, dynamic range, imaging speed, contrast enhancement and safety. Computed Xray tomography and Radioisotopes: Basic principles. 
PH30036: Final year project  A 
Credits: 6 
Level: Honours 
Semester: 1 
Assessment: OT100 
Requisites: 
After taking this unit you must take PH30037 
Aims & Learning Objectives: The aims of this unit are to provide students with the opportunity to investigate in depth some aspect or application of physics, to develop experimental and/or computational skills complementary to those developed in formal lecture courses, and to give students firsthand experience of innovation and/or research. While taking this unit, the student should be able to: * demonstrate enthusiasm, industry and motivation in carrying out the project, as well as good time management skills in allocating appropriate amounts of time to the project; * thoroughly research the background to the project using academic journals, textbooks and computerbased resources; * for an experimental project, demonstrate good practical skills in the construction of apparatus and circuits and in data measurement and analysis; * for a computational project, design, write and test computer programs to simulate the physical system under study, and interpret the results from these programs; * demonstrate some innovation and initiative, as well as a basic understanding of the theory and background to the project; * make a short oral presentation to the tutor at the end of the unit, describing the background to the project and any results obtained to date. Content: Final year projects offered cover a wide range of physics and most reflect the research interests of academic staff. Many are related to the Department's externally sponsored research projects (funded by the Research Councils, public companies, and UK government or EU agencies). Each year a few projects are carried over from students' industrial placements. A few projects are concerned with the development of undergraduate experiments. 
PH30037: Final year project  B 
Credits: 6 
Level: Honours 
Semester: 2 
Assessment: PR67OR33 
Requisites: 
Before taking this unit you must take PH30036 
Aims & Learning Objectives: The aims of this unit are to provide students with the opportunity to investigate in depth some aspect or application of physics, to develop experimental and/or computational skills complementary to those developed in formal lecture courses, and to give students firsthand experience of innovation and/or research. While taking this unit, the student should be able to: * demonstrate enthusiasm, industry and motivation in carrying out the project, as well as good time management skills in allocating appropriate amounts of time to the project and for the planning, research and writing of the report; * for an experimental project, demonstrate good practical skills in the construction of apparatus and circuits and in data measurement and analysis; * for a computational project, design, write and test computer programs to simulate the physical system under study, and interpret the results from these programs; * demonstrate some innovation and initiative, as well as a basic understanding of the theory and background to the project; * write a detailed technical report on the project, giving the background and theory behind the work, describing the work carried out and the results obtained and displaying an appropriate level of technical content, style and structure; * demonstrate the ability to answer questions on the work carried out in the project and on the report in a viva examination. Content: Student continues work of PH30036. 
PH30054: Quantum mechanics (distance learning) 
Credits: 12 
Level: Honours 
Academic Year 
Assessment: EX 
Requisites: 
While taking this unit you must take PH40041 
Aims & Learning Objectives: The aims of this unit are to show how a mathematical model of considerable elegance may be constructed, from a few basic postulates, to describe the seemingly contradictory behaviour of the physical universe and to provide useful information on a wide range of physical problems. After taking this unit the student should be able to: * discuss the dual particlewave nature of matter; * explain the relation between wave functions, operators and experimental observables; * justify the need for probability distributions to describe physical phenomena; * set up the Schroedinger equation for simple model systems; * derive eigenstates of energy, momentum and angular momentum; * apply approximate methods to more complex systems. Content: Introduction: Breakdown of classical concepts. Old quantum theory. Quantum mechanical concepts and models: The "state" of a quantum mechanical system. Hilbert space. Observables and operators. Eigenvalues and eigenfunctions. Dirac bra and ket vectors. Basis functions and representations. Probability distributions and expectation values of observables. Schrödingers equation: Operators for position, time, momentum and energy. Derivation of timedependent Schrödinger equation. Correspondence to classical mechanics. Commutation relations and the Uncertainty Principle. Time evolution of states. Stationary states and the timeindependent Schrödinger equation. Motion in one dimension: Free particles. Wave packets and momentum probability density. Time dependence of wave packets. Bound states in square wells. Parity. Reflection and transmission at a step. Tunnelling through a barrier. Linear harmonic oscillator. Motion in three dimensions: Stationary states of free particles. Central potentials; quantisation of angular momentum. The radial equation. Square well; ground state of the deuteron. Electrons in atoms; the hydrogen atom. Hydrogenlike atoms; the Periodic Table. Spin angular momentum: Pauli spin matrices. Identical particles. Symmetry relations for bosons and fermions. Paulis exclusion principle. Approximate methods for stationary states: Time independent perturbation theory. The variational method. Scattering of particles; the Born approximation. 
PH30055: Computational physics A 
Credits: 6 
Level: Honours 
Semester: 1 
Assessment: CW75OR25 
Requisites: 
Before taking this unit you must take PH20018 
Students should have taken an appropriate selection
of year 1 and year 2 physics units, including PH20018 in order to take this
unit. Aims & Learning Objectives: The aims of this unit are to introduce students to the practical use of computer modelling as a complement to theoretical and experimental solution of physical problems, to introduce some of the contemporary packages available to the modeller, and to explore topics in physics which lend themselves to computational modelling. After taking this unit the student should be able to: * Identify the strengths and weaknesses of a computational approach to modelling; * Use existing packages to demonstrate topics in undergraduate physics; * Construct Maple worksheets to analyse physical problems; * Perform simple simulations using 2d cellular automata; * Explain the methodology and output of the simulations performed. Content: Introduction to simulation as a means of gaining physical insight; contemporary applications of simulation; practical uses of simulation packages. Computer algebra packages as a scientific computer environment; problems solved effectively in this environment and those not. Practical introduction to Maple. Exercises and projects based upon construction of Maple worksheets, analysing physical problems. Examples may include timedependent quantum mechanical scattering, coupled oscillators, resonant phenomena, simple nonlinear (including chaotic) systems, timeseries analysis. Introduction to cellular automata, selforganisation and fractals. Applications to physical systems. Exercises and projects including interfacing to computer graphics. 
PH30056: Computational physics B 
Credits: 6 
Level: Honours 
Semester: 2 
Assessment: CW75OR25 
Requisites: 
Before taking this unit you must take PH20018 
Aims & Learning Objectives: The aim of this unit is to provide students with experience in the application of some of the techniques widely used in the simulation of physical systems, and to develop their ability at using computers in physical modelling. Topics will be chosen for study which encourage a greater understanding of both the model and the underlying physics. The emphasis will be on the application and interpretation of the techniques, not on programming. After taking this unit the student should be able to: * identify issues which influence the choice of language and architecture; * interface C programs to a 2d graphics package; * outline the physics and computational issues illustrated by the Ising model; * develop finite difference and finite element simulations of given systems; * discuss issues involved in the use of basis set methods; * explain the methodology and output of the simulations performed. Content: Overview of computer languages for scientific work; computer architecture and code optimisation. Revision of C programming in the UNIX environment. Simulation of systems with many degrees of freedom: The Ising model. Finite size effects, fluctuations, correlations, phase transition, thermal equilibrium state, evaluation of observables. Numerical solution of partial differential equations. Application and exploration of finite difference and finite element programs. Visualisation of solutions. Application to contemporary problems. Basis set methods. Illustration and comparison of computational schemes. 
PH30057: Stellar & galactic astrophysics 
Credits: 6 
Level: Honours 
Semester: 1 
Assessment: EX80CW20 
Requisites: 
Before taking this unit you must take PH10001 and take PH10004 and take PH10007 and take PH10008 and take PH20013 or their equivalents. 
Aims & Learning Objectives: The aims of this unit are to explore the physical processes that lead to the formation and evolution of stars and to the structure and chemical evolution of galaxies. An additional aim is that certain core physics material from the first and second years should be strengthened through study of these astrophysical topics. After taking this unit the student should be able to * recognise how observations made across the EM spectrum yield information on astrophysical phenomena and that the techniques used have limitations * describe the structure and dynamics of galaxies and how they are related * outline the key steps in the formation and evolution of galaxies * describe the physical processes occurring in the interstellar medium * discuss in detail how stars form from gravitational collapse of dense gas clouds * solve order of magnitude problems on any part of the syllabus. Content: Galactic Astrophysics; Morphology & Classification. Constituents and observational properties of galaxies. TullyFisher relation. The fundamental plane. Galactic rotation formulae. Surface brightness. The galaxy luminosity function. Observational selection effects. Galaxies and the Universe. Standard candles and the distance ladder. Clusters and superclusters. Evidence for dark matter. Galaxy formation. Jeans instability. The chemical evolution of galaxies. Observations of high redshift protogalaxies. Stellar Astrophysics; Components of the ISM. Dark clouds. HII regions. TTauri stars. HH objects. Masers. Angular momentum and magnetic field problems. Obtaining information about the ISM. Spectral line shapes. Interstellar reddening. Optical depth. Dust grains. Formation of molecules. Radiatively excited regions. Continuum emission. Hydrostatic equilibrium. Collapse processes. Star formation. Evolution of protostars. Molecular outflows. Zeroage main sequence stars. Evolution off the main sequence. Late stages of stellar evolution. Supernovae. Stellar remnants. 
PH40038: MPhys laboratory A 
Credits: 6 
Level: Masters 
Semester: 1 
Assessment: CW100 
Requisites: 
After taking this unit you must take PH40039 and before taking this unit you must take PH20021 and take PH20022 and take PH30036 and take PH30037 
Aims & Learning Objectives: The aim of this unit is to develop skills involved with data collection, analysis and interpretation through performing three extended experiments with researchgrade apparatus. While taking this unit the student should be able to: * perform necessary background reading and planning; * become familiar with the safe and effective use of advanced equipment; * use appropriate methods for signal reduction and data analysis; * demonstrate enthusiasm, industry and motivation in carrying out the experiments and managing the available time; * keep a laboratory logbook and prepare a report on each experiment performed; * be able to consider and to propose further extension or development of the experiments performed. Content: A number of experiments will be offered, most reflecting the research interests of academic staff. Three will be chosen, each lasting four days. 
PH40039: MPhys laboratory B 
Credits: 6 
Level: Masters 
Semester: 2 
Assessment: CW100 
Requisites: 
Before taking this unit you must take PH20021 and take PH20022 and take PH40038 
Aims & Learning Objectives: The aim of this unit is to develop skills required to prepare and write a Case Study, and to perform an extended experiment based on one of the experiments performed in PH40038. While taking this unit the student should be able to: * carry out a survey of research literature and other resources, to provide background material for the Case Study and to plan elements of the extended experiment; * produce a wellwritten and wellconstructed Case Study covering the physics of the chosen experiment and the experimental plan for its extension; * show initiative in developing the experiment; * modify or develop apparatus and/or advanced techniques of data analysis, in consultation with members of staff; * competently manage time and resources to ensure the timely completion of the extended experiment; * write a detailed technical report on the extended experiment, displaying an appropriate level of content, style and structure. Content: In the first third of the unit a case study is prepared and written, including a literature review and making proposals for significant extension of one of the experiments performed in PH40038. In the remainder of the unit the extended experiment is performed and a technical report written. 
PH40041: M.Phys. placement 
Credits: 48 
Level: Masters 
Academic Year 
Assessment: OT100 
Requisites: 
While taking this unit you must take PH30054 
Aims & Learning Objectives: The aims of this unit are for MPhys students to carry out an identifiable and original part of an approved research project or other professional activity whilst placed at an approved laboratory or other organisation, and to develop the personal and technical skills needed by a professional physicist working in an advanced technical environment. On completion of this unit, the student should have demonstrated: * the ability to apply knowledge and skills gained at the university to an original part of a technical project in a professional context; * sustained intellectual effort and initiative in solving technical problems; * good personal skills in planning and time management, problem solving, decision making and team membership, to the satisfaction of the internal supervisor; * good oral communication and presentation skills, including making an oral presentation on the project and the host laboratory at the placement conference; * the ability to write a case study report describing the activities and structure of the employing organisation, and the significance of their project in its overall strategy; * the ability to write a technical report describing the work carried out by the student on the placement, highlighting the relevance of their project to the organisation, and the student's particular role in the project; * the ability to answer questions about the host organisation and technical details of the project at a viva examination. Content: The content varies from placement to placement. In choosing the placement, the university will try to ensure that the project offers adequate opportunities for the student to demonstrate competence in the following categories: Self management and development, Managing tasks, Communicating clearly and effectively, Working with and relating to others, Applying knowledge, Applying initiative in work problems, Practical ability and/or Computational Skill 
PH40043: MPhys year abroad 
Credits: 60 
Level: Masters 
Academic Year 
Assessment: OT100 
Requisites: 
Aims & Learning Objectives: The aims of this unit are for students to gain experience of living and studying in a University outside the UK and to develop the appropriate personal and linguistic skills skills, in addition to developing their knowledge and understanding of physics and mathematics. While taking this unit, the student should: * develop personal and interpersonal communication skills and the ability to work and interact effectively in a group environment in which cultural norms and ways of operating may be very different from those previously familiar; * develop the selfconfidence and maturity to operate effectively with people from a different cultural background; * develop an understanding of the stresses that occur in working in a different culture from the UK, and learn to cope with those stresses; * in the case of students attending Universities in countries whose language is not English, improve their knowledge of the host language by attending classes therein; * in the case of students attending lectures in a language other than English, develop the ability to operate at a high scientific level in the language of the country concerned; this would include oral communication and comprehension as well as reading and writing. Content: It is assumed that the student abroad will accomplish work equivalent to 60 University of Bath credits (i.e. 10 units). Details of those are necessarily left to negotiation with individual Universities, students and the Bath Director of Studies but a sample study programme might be : EUROPE : Academic units: 36 credits (6 units); Management: 6 credits (1 unit); Research project: 12 credits (2 units); Language work: 6 credits (1 unit). USA : Academic units: 42 credits (7 units); Management : 6 credits (1 unit); Research project: 12 credits (2 units); Language work: 0. Among the Academic units there should be units equivalent to those taken by students on the Bath fulltime MPhys course. 
PH40045: Advanced topics Yr 3 
Credits: 6 
Level: Masters 
Semester: 1 
Assessment: EX80CW20 
Requisites: 
Aims & Learning Objectives: The aim of this unit is to extend the breadth and depth of knowledge of MPhys students by introducing them to a number of more advanced topics on Physics and Mathematics. As the content of this unit varies from year to year, it is not possible to define specific learning objectives. Content: The unit will run on a twoyearly basis and will consist of two or three courses in each year. The courses will tend to reflect the research interests of staff members in the Department of Physics. Possible courses include: Theory of complex variables; Quantum nanostructure devices; Fluid dynamics; Advanced quantum theory; Acoustic scattering theory; Group theory; Tensor properties of solids; Remote sensing principles. 
PH40058: Advanced topics Yr 4 
Credits: 6 
Level: Masters 
Semester: 1 
Assessment: EX80CW20 
Requisites: 
Aims & Learning Objectives: The aim of this unit is to extend the breadth and depth of knowledge of MPhys students by introducing them to a number of more advanced topics on Physics and Mathematics. As the content of this unit varies from year to year, it is not possible to define specific learning objectives. Content: The unit will run on a twoyearly basis and will consist of two or three courses in each year. The courses will tend to reflect the research interests of staff members in the Department of Physics. Possible courses include: Theory of complex variables; Quantum nanostructure devices; Fluid dynamics; Advanced quantum theory; Acoustic scattering theory; Group theory; Tensor properties of solids; Remote sensing principles. 
