UNIT CATALOGUE |

PHYS0001: Introduction to quantum physics
Semester 1
6
Credits: Contact:
Level: Level 1
Assessment: EX80 CW20
Requisites: Students must have A-level 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 wave-particle 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 alpha-particles and Rutherford's model. Photons and energy quantisation: Black-body radiation; the ultraviolet catastrophe and Planck's hypothesis. Photoelectric effect. The electromagnetic spectrum. X-rays. Compton scattering. Sources of photons; the Bohr model of the atom. Deficiencies of Bohr's model. Wave-particle duality: An introduction to waves. Wave-like 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. |

PHYS0002: Properties of matter
Semester 1
6
Credits: Contact:
Level: Level 1
Assessment: EX80 CW20
Requisites: Students must have A-level Physics or Chemistry and A-level 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, X-ray scattering and Bragg's law. First and second laws of thermodynamics, P-V-T 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 non-Newtonian) in liquids based on cage models. |

PHYS0003: Introduction to electronics
Semester 1
6
Credits: Contact:
Level: Level 1
Assessment: EX80 CW20
Requisites: Ex PHYS0050 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 flip-flops * 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: one-way valve, piece-wise 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, non-inverting and differential amplifiers, addition and subtraction, differentiation, integration, buffer amplifiers. Blackbox treatment of amplifiers; input, output and transfer characteristics. Characteristics of ideal and real op-amps. 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 op-amps. (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 flip-flop and JK flip-flop. Shift register. Ripple counter. (8 lectures). Digital-to-Analogue and Analogue-to-Digital Converters: Binary weighted and R-2R DACs. Flash ADCs. (1 lecture). |

PHYS0004: Relativity & astrophysics
Semester 2
6
Credits: Contact:
Level: Level 1
Assessment: EX80 CW20
Requisites: Students must have A-level 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 large-scale structure - solve simple problems concerning orbital motion, blackbody radiation, cosmological redshift, stellar luminosity and magnitude. Content: Special Relativity: Galilean transformation. Speed of light - Michelson-Morley 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 : X-rays, gamma-rays, infrared and radio astronomy. Gravitation: Gravitational force and potential energy. Weight and mass. Circular orbits; Kepler's Laws; planetary motion. Escape velocity. Solar System: Earth-Moon 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; black-body radiation; stellar classification; Hertzsprung-Russell 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. |

PHYS0005: Mechanics & waves
Semester 2
6
Credits: Contact:
Level: Level 1
Assessment: EX80 CW20
Requisites:
Pre PHYS0007Aims & 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 one-dimensional 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 one-dimensional structures - derive and apply the formulae for the non-relativistic 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 non-constant acceleration. Linear momentum, collisions, rockets. Work and Energy: potential energy, conservative and non-conservative 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 non-dispersive waves, phase and group velocity. Beats. Doppler effect. |

PHYS0006: Electricity & magnetism
Semester 2
6
Credits: Contact:
Level: Level 1
Assessment: EX80 CW20
Requisites:
Pre PHYS0007Aims & 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 current-carrying wire, force between current-carrying wires, torque on a current loop, magnetic dipoles. Biot-Savart 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. |

PHYS0007: Mathematics for scientists 1
Semester 1
6
Credits: Contact:
Level: Level 1
Assessment: EX80 CW20
Requisites: Students must have A-level 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 A-level 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, reiq 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. |

PHYS0008: Mathematics for scientists 2
Semester 2
6
Credits: Contact:
Level: Level 1
Assessment: EX80 CW20
Requisites:
Pre PHYS0007Aims & 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 A-level 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, Runge-Kutta 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. |

PHYS0009: Consolidation mathematics A
Semester 1
3
Credits: Contact:
Level: Level 1
Assessment: CW100
Requisites: Co PHYS0010 Aims & Learning Objectives: The aim of this unit is to remedy lacunae in the mathematical abilities of those students entering the first year of the Physics course without a C grade in A level maths or its equivalent, by revisiting parts of the Mathematics A-level syllabus and consolidating the work being carried out in PHYS0007. After taking this unit, the student should be able to - demonstrate adept algebraic manipulation of simple equations and solve quadratic equations - write down the magnitude of a vector and the dot and cross product of two vectors - convert between cartesian and polar co-ordinates and between the cartesian, polar and exponential notations for complex numbers - add and multiply complex numbers in cartesian, polar and exponential forms - calculate binomial coefficients and write down binomial expansions - solve simple problems involving exponential and logarithm functions - differentiate simple functions using the product, quotient and function of a function rules, logarithmic differentiation and implicit functions. Content: Algebraic manipulation Vectors Polar co-ordinates and complex numbers Binomial Expressions Exponential and Log functions Differentiation: products, implicit, logarithmic. |

PHYS0010: Consolidation mathematics B
Semester 2
3
Credits: Contact:
Level: Level 1
Assessment: CW100
Requisites: Co PHYS0009 Aims & Learning Objectives: The aim of this unit is to remedy lacunae in the mathematical abilities of those students entering the first year of the Physics course without a C grade in A level maths or its equivalent, by revisiting parts of the Mathematics A-level syllabus and consolidating the work being carried out in PHYS0007 and PHYS0008. After taking this unit, the student should be able to - write down the partial derivative of a function of several variables - integrate functions by substitution, by partial fractions and by parts and apply integration techniques to simple physical problems - solve simple double integral problems - solve 1st order ordinary differential equations by means of separation of variables and an integrating factor and apply ordinary differential equations to simple physical problems - evaluate the determinant of a matrix. Content: 1st order Ordinary Differential Equations Further Vectors Applied Differential Equations Double Integration Determinants Miscellaneous problems. |

PHYS0011: Laboratory & information skills - 1A
Semester 1
6
Credits: Contact:
Level: Level 1
Assessment: PR90 CW10
Requisites: 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 self-paced 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 small-scale 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 small-scale experimental investigation. The topic is chosen from a wide range of physics appropriate to first-year 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. |

PHYS0012: Laboratory & information skills - 1B
Semester 2
6
Credits: Contact:
Level: Level 1
Assessment: PR80 OT20
Requisites:
Pre PHYS0011Aims & Learning Objectives: The aim of this unit is to build on the basic laboratory skills developed in PHYS0011, 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 small-scale 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 PHYS0011 - 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: Mini-project to design, construct and test a basic digital system. Project: A second independent project, similar in nature to that in PHYS0011. 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. |

PHYS0013: Quantum & atomic physics
Semester 1
6
Credits: Contact:
Level: Level 2
Assessment: EX80 CW20
Requisites:
Pre PHYS0001,
Pre PHYS0008Natural science students must have taken PHYS0048 in order to undertake this unit. PHYS0001 and PHYS0005 are desirable as pre-requisites but not essential. Aims & Learning Objectives: 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 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. Schrödinger equation: time dependence of the wave function. Time-independent 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 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. Electron-electron interactions: screening and exchange interaction. Chemical bonding. Nomenclature for labelling atomic configurations and terms. Hund's rules. Fine structure and Zeeman effect in many-electron atoms. Factors affecting width of spectral lines and introduction to high resolution spectroscopy. |

PHYS0014: Electromagnetic waves & optics
Semester 1
6
Credits: Contact:
Level: Level 2
Assessment: EX80 CW20
Requisites:
Pre PHYS0008Natural science students must have taken PHYS0051 and PHYS0053 in order to undertake this unit. PHYS0005 and PHYS0006 are desirable, but not essential, pre-requisites 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 multiple-beam interference and hence interpret the output from a Fabry-Pérot 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 Mach-Zehnder interfermoters. Anti-reflection coatings. The Fabry-Perot 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 far-field 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. |

PHYS0015: Semiconductor physics & devices
Semester 1
6
Credits: Contact:
Level: Level 2
Assessment: EX80 CW20
Requisites: PHYS0007, PHYS0003, PHYS0011 and PHYS0012 are desirable, but not essential pre-requisites for this unit.
Aims & Learning Objectives: The aims of this unit are to provide an introduction to analogue electronics and device physics and to introduce the fundamental ideas of semiconductor physics in a qualitative manner, leading to descriptions of the action of semiconductor devices, such as the pn junction diode and FET. After taking this unit the student should be able to * demonstrate the use of load lines in determining circuit operation * explain the concept of negative feedback in electronic circuits * design and perform calculations on simple transistor circuits * outline the principles of digital control and data acquisition * account for the formation of the depletion region at a pn junction and for FET operation by means of a qualitative description of semiconductor device physics * sketch the processing steps involved in the fabrication of a bipolar junction and field effect transistor. Content: Semiconductor physics: Lattice structure, concepts of holes and energy gap as energy required to break covalent bonds. Conduction and valence bands. Extrinsic and intrinsic semiconductors, concept of binding energy - Fermi level and Fermi-Dirac statistics. Density of states, semiconductor statistics and Law of Mass Action. Conduction properties: scattering mechanisms, mobility, drift velocity, resistivity, diffusion. Einstein relation. Recombination processes, surface recombination. Optical, thermal and high field properties, decay of photoexcited carriers. Basic equations of semiconductor device operation: current density equations and continuity equations. (9 lectures). The p-n junction: The unbiased p-n junction: junction formation, built-in potential, charge and electric field profiles, depletion layer width. The p-n junction under bias: effect of bias on drift and diffusion currents, band profiles and depletion region width. Junction capacitance. Ideal diode equation. Reverse breakdown. (5 lectures). Junction field effect transistor: Amplification by means of transistors. Internal structure of JFET. Electrical characteristics of n-channel JFET. Pinch off, saturation, breakdown. Biassing JFETs, load lines. Small signal analysis and equivalent circuit. Transconductance. Analysis and design of common source amplifier including frequency response. Source follower. Differential amplifier. (5 lectures). Bipolar junction transistor: Internal structure of BJT. Qualitative description of internal operation. Current gain, transfer characteristic, output characteristic for common emitter configuration. (2 lectures). Semiconductor device fabrication: Relevant properties of Silicon, GaAs and SiO2. Crystal growth. Doping: diffusion and ion implantation. Epitaxial growth: MBE and MOCVD. Lithography, oxidation, etching and metallisation. Fabrication of simple devices. (3 lectures). |

PHYS0016: Building blocks of the universe
Semester 2
6
Credits: Contact:
Level: Level 2
Assessment: EX80 CW20
Requisites:
Pre PHYS0013Natural science students must have taken PHYS0049 in order to undertake this unit. 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, half-life and mean lifetime, generation and decay. Particle kinematics and the discovery of the neutrino. Elementary Particles: Quarks, leptons and mediators. Anti-particles. 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: Beta-decay. Electron and positron emission; K-capture. Alpha decay : energetics and simplified tunnelling theory. The liquid drop model and semi-empirical 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 re-visited. Separation of unified forces. Inflation theory. Formation of elementary particles. Cosmic nucleosynthesis. Dark matter in the universe. MACHOs, WIMPs and Winos. |

PHYS0017: Introduction to solid state physics
Semester 2
6
Credits: Contact:
Level: Level 2
Assessment: EX80 CW20
Requisites:
Pre PHYS0002,
Pre PHYS0008,
Pre PHYS0005,
Pre PHYS0013Aims & 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 - describe how allowed and forbidden energy bands arise - describe how the properties of electrons in allowed energy bands determine the behaviour of conducting and semiconducting solids - describe how band structure theories lead to concepts such as effective mass and how these are related to densities of states and carrier concentrations - describe the factors that control the mobility and electrical conductivity - describe 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 X-rays and of neutrons is related to the properties of the reciprocal lattice and solve simple problems associated with the determinations of crystal structures Content:Classification of solids. Bonding forces; allowed and forbidden energy bands. Basic crystal structures; translational symmetry; space lattices; unit cells; Miller indices. The classical free electron theory and its failure. The quantum free electron theory. 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; electron and hole concentrations and the effects of doping; donors and acceptors. Transport properties: electrical conduction and scattering of electrons and holes in solids; the Hall effect; cyclotron resonance. Diffraction of waves in crystalline structures; Bragg law; the reciprocal lattice and Brillouin zones. X-ray and neutron diffraction studies of crystal structures. The interaction of light with solids. |

PHYS0018: Programming skills
Semester 2
6
Credits: Contact:
Level: Level 2
Assessment: CW60 EX40
Requisites: Aims & Learning Objectives: The aims of this unit are to introduce and develop structured programming skills in a high-level 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 introduced in PHYS0007 and PHYS0008 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 round-off 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; root-finding; function evaluation via series expansion and look-up 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. |

PHYS0019: Mathematics for scientists 3
Semester 1
6
Credits: Contact:
Level: Level 2
Assessment: EX80 CW20
Requisites:
Pre PHYS0008Aims & 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' problem-solving 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. |

PHYS0020: Mathematics for scientists 4
Semester 2
6
Credits: Contact:
Level: Level 2
Assessment: EX80 CW20
Requisites:
Pre PHYS0019Aims & 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' problem-solving 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 o derive theorems of analytic functions and use them to evaluate integrals. 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 source-free vacuum. Plane wave solutions. OR Functions of a complex variable (8 hours): Differential functions, analytic functions, singularities, Cauchy-Riemann equations, power series in a complex variable, elementary functions, principal values, branch cuts. Complex integration; Cauchy's theorem and integral, zeroes and poles, Laurent expansion, residue theorem, principal value of an integral, Jordan's lemma, integration of simple functions, summation of series. |

PHYS0021: Laboratory & information skills 2A
Semester 1
6
Credits: Contact:
Level: Level 2
Assessment: PR100
Requisites:
Pre PHYS0011,
Pre PHYS0012,Co PHYS0022 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 PHYS0013, PHYS0014 and PHYS0015 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, x-rays, electromagnetism, analogue electronics, instrumentation and ultrasonics. These activities will be underpinned by workshops on writing skills and scientific computer packages. |

PHYS0022: Laboratory & information skills 2B
Semester 2
6
Credits: Contact:
Level: Level 2
Assessment: PR100
Requisites: Co PHYS0021 Aims & Learning Objectives: The aims of this unit are to build on the laboratory and written presentation skills developed in PHYS0021 and to develop the skills required for preparing and delivering oral presentations. An additional aim is to reinforce elements of unit PHYS0017 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 small-scale 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, x-rays, electromagnetism, analogue electronics and ultrasonics. These activities will be underpinned by a workshop on oral presentation skills. |

PHYS0023: Electromagnetism
Semester 1
6
Credits: Contact:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Pre PHYS0020,
Pre PHYS0014Aims & 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 time-varying 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 time-varying fields - calculate and make use of the electromagnetic Poynting vector - use static and time-varying 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 (cut-off, 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, Biot-Savart 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. |

PHYS0024: Contemporary physics
Semester 1
6
Credits: Contact:
Level: Level 3
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 computer-based 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 |

PHYS0025: Equations of science
Semester 2
6
Credits: Contact:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Pre PHYS0007,
Pre PHYS0008,
Pre PHYS0019,
Pre PHYS0020Aims & 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 non-linear, 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 non-linear 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 non-linear equations, and analyse non-linear ordinary differential equations - analyse one-dimensional 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. Non-linearity and chaos (12 hours): Examples of non-linearity in the natural sciences; Non-linear wave equations, solitary waves, physical examples. Nonlinear differential equations: phase space, trajectories, fixed points, bifurcation. Examples from the natural sciences. Non-linear difference equations: orbits, cobwebs, fixed points, bifurcations, chaos. Examples from the natural sciences. |

PHYS0027: Signals & measurement systems
Semester 1
6
Credits: Contact:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Pre PHYS0003,
Pre PHYS0019,
Pre PHYS0003Aims & Learning Objectives: The aims of this unit are to introduce concepts of noise, methods of recovering signals from noise, sampled signals, the artefacts generated by sampling and digital signal processing. A further aim is to show through a detailed study of specific examples how the basic building blocks of feedback measurement and control systems can be chosen and assembled and the static and dynamic performance analysed. After taking this unit the student should be able to - identify common noise sources and estimate their values in a given experiment - evaluate the information content of a sampled signal - design simple digital filters with a desired frequency response - design and develop mathematical models for feedback systems and explain their advantages for measurement and control - choose and describe appropriate signal recovery techniques for a particular application and make quantitative estimates of the advantages in certain cases. Content: Noise and random signals. Noise sources: thermal noise, shot noise and 1/f noise. Noise calculations. Signal to noise ratio. AC measuring techniques and signal recovery methods: filtering, averaging and phase sensitive detection. Lock-in amplifier, box-car integrator and multichannel averager. Correlation techniques. Sampled signals and the sampling theorem. Discrete Fourier transform. Fundamental interval and aliasing. Resolution. Discontinuities and spectral leakage. Laplace transform and its role in signal processing. Correlation and autocorrelation convolution. Introduction to digital signal processing, z- transform. Design of digital filters using z- and Fourier transforms Introduction to sensor and transducer technologies. Feedback, and its application to measurement and control systems. Static and dynamic theory of feedback. Case studies of instrumentation systems e.g. Frequency and amplitude stabilisation of a laser. Fluxgate magnetometer. Tunnelling microscope. |

PHYS0028: Solids & surfaces
Semester 1
6
Credits: Contact:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Pre PHYS0017,
Pre PHYS0020Aims & Learning Objectives: The aims of this unit are to introduce some of the main ways in which real materials differ from perfect, infinite crystals at zero temperature, and to relate the imperfections to macroscopic material properties. After taking this unit the student should be able to - solve simple technological and fundamental problems involving the thermal and acoustic properties of crystals and glasses - account for the vibrational properties of solids - solve structural and vibrational problems in the reciprocal lattice and k-space - relate the electronic, optical and mechanical properties of real crystals to their defects - 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 surface experimental probes. Content: Lattice vibrations: dynamics of linear, monatomic and diatomic chains, dispersion relations, acoustic and optic vibrations. Extension to three-dimensional crystals. Quantisation and phonons, crystal momentum. Study of phonons by inelastic neutron and light scattering and ultrasonics: elastic constants. Thermal properties of insulating crystals; lattice contribution to specific heat; Debye approximation. Vibrational anharmonicity and thermal conductivity. Dielectric and optical properties. Scattering of electrons by phonons, temperature dependence of electrical conductivity. Phase transitions and lattice dynamics. Introduction to amorphous solids. Topological disorder. Determination of glass structure by EXAFS. Short range order, vibrational states and thermal conductivity of glasses. 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. Surface physics: importance of surfaces, eg catalysis, corrosion, epitaxial growth. Clean and real surafaces. Surface energy. Surface crystal structure; relaxation and reconstruction; Wood notation. Surface electronic structure; the work function, 2-band model of surface states; adsorbates. Experimental probes; electron spectroscopies, low energy electron diffraction, scanning tunnelling microsopy. |

PHYS0029: Thermodynamics & statistical mechanics
Semester 2
6
Credits: Contact:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Pre PHYS0002,
Pre PHYS0008Aims & Learning Objectives: The aims of this unit are 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 p-V 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 Fermi-Dirac, Bose-Einstein, 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, Gibbs-Duhem relation, equilibrium between phases and the Clausius-Clapeyron 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 two-state 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. Fermi-Dirac and Bose-Einstein distribution functions and their classical limit. Properties of Fermi systems: ground state of a Fermi gas, density of states, Fermi gas at non-zero temperature, electrons in solids, model of a neutron star. Properties of Bose systems: Bose-Einstein condensation, superfluidity, Planck distribution function and Stefan-Boltzmann 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. |

PHYS0030: Quantum mechanics
Semester 2
6
Credits: Contact:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Pre PHYS0007,
Pre PHYS0008,
Pre PHYS0019,
Pre PHYS0020A-level 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 time-dependent Schrodinger equation. Correspondence to classical mechanics. Commutation relations and the Uncertainty Principle. Time evolution of states. Stationary states and the time-independent 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. Hydrogen-like 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. |

PHYS0031: Simulation techniques
Semester 1
6
Credits: Contact:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Pre PHYS0020Aims & 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; de-dimensionalisation, 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 Monte-Carlo Methods; examples of N-body 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 non-linear least squares fitting. |

PHYS0032: Lasers & modern optics
Semester 2
6
Credits: Contact:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Pre PHYS0023,
Pre PHYS0013,
Pre PHYS0017Aims & 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 multi-element systems of lenses and mirrors - describe and analyse the interactions between light and matter that lead to spontaneous emission and lasing in 3- and 4-level systems - treat cw, mode-locked and Q-switched 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 quarter-wave 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 self-phase 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, line-widths and broadening, Q switching and mode locking. Manipulation of light: Dielectric waveguides, optical fibres, dispersion of short pulses, second and third order nonlinear optics, electro-optic modulation, solitons. |

PHYS0033: Low-dimensional semiconductors
Semester 2
6
Credits: Contact:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Pre PHYS0023,
Pre PHYS0015,
Pre PHYS0013,
Pre PHYS0017Aims & Learning Objectives: 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: Electron-photon interaction in semiconductors. Optical absorption in bulk semiconductors: spectral dependence, photocurrent, P-I-N photodiodes, avalanche detectors, solar cells. Optical absorption in quantum wells: interband and intersubband transitions, selection rules. Excitons in bulk semiconductors and quantum wells. Quantum-confined Stark effect and quantum well modulators. Optical emission in semiconductors: radiative and non-radiative transitions, light-emitting 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. |

PHYS0034: Complex states of matter
Semester 2
6
Credits: Contact:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Pre PHYS0017Aims & Learning Objectives: The aim of this unit is to explain the basic properties of superconductivity, superfluidity and magnetism. 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 - outline the basic properties of superfluidity in Helium-4 - describe theoretical models for superfluidity in Helium-4 - derive the Curie-Weiss law of paramagnetism and use it to explain the ferromagnetic state - express the free energy of a simple, ordered magnetic system in terms of the state variables and relevant parameters - explain the magnetisation process and hysteresis in terms of standard domain models. Content: Superconductivity; basic phenomena of superconductivity: critical temperature, zero resistance, critical magnetic field, Meissner effect, penetration depth, coherence length. Two fluid model. Ginsburg-Landau theory. Microscopic theory, Cooper pairs, electron phonon interaction, isotope effect, BCS model and the energy gap. Type I and type II superconductors, the mixed state. Applications of type II materials. Tunnelling in superconductors, the Josephson effect. High Tc superconductivity. The Helium dilution refrigerator. The physics of the superfluid state. Superfluidity; properties of liquid Helium-4, superfluidity in Helium-4, London and Landau models. Differences between Helium-4 and Helium-3. Introduction to solid state magnetism and models of magnetic crystals; Heisenberg model. Ferromagnetism; the magnetisation process, anisotropy, domain structure, hysteresis loops, magnetisation dynamics and magnetostriction. Hard and soft materials and their applications. |

PHYS0035: Medical physics
Semester 2
6
Credits: Contact:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Pre PHYS0008,
Pre PHYS0014,
Pre PHYS0016Aims & 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: 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 cross-sectional images of tissue properties, and function, using nuclear magnetic resonance imaging. Spatial resolution, dynamic range, imaging speed, contrast enhancement and safety. Computed X-ray tomography and Radioisotopes: Basic principles. |

PHYS0036: Final year project - A
Semester 1
6
Credits: Contact:
Level: Level 3
Assessment: OT100
Requisites: Co PHYS0037 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 first-hand 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 computer-based 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. |

PHYS0037: Final year project - B
Semester 2
6
Credits: Contact:
Level: Level 3
Assessment: PR67 OR33
Requisites: Co PHYS0036 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 first-hand 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 PHYS0036. |

PHYS0038: MPhys laboratory A
Semester 1
6
Credits: Contact:
Level: Undergraduate Masters
Assessment: CW100
Requisites:
Pre PHYS0021,
Pre PHYS0022,
Pre PHYS0036,
Pre PHYS0037Aims & Learning Objectives: The aim of this unit is to develop skills involved with data collection, analysis and interpretation through performing three extended experiments with research-grade 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. |

PHYS0039: MPhys laboratory B
Semester 2
6
Credits: Contact:
Level: Undergraduate Masters
Assessment: CW100
Requisites:
Pre PHYS0038Aims & 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 PHYS0038 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 well-written and well-constructed 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 PHYS0038. In the remainder of the unit the extended experiment is performed and a technical report written. |

PHYS0040: B.Sc. placement
Academic Year
60
Credits: Contact:
Level: Level 2
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. |

PHYS0041: M.Phys. placement
Academic Year
48
Credits: Contact:
Level: Undergraduate Masters
Assessment: OT100
Requisites: Co PHYS0054 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 |

PHYS0042: BSc year abroad
Academic Year
60
Credits: Contact:
Level: Level 2
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 self-confidence 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. |

PHYS0043: MPhys year abroad
Academic Year
60
Credits: Contact:
Level: Undergraduate Masters
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 self-confidence 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 USA* Academic units 36 credits (6 units) 42 credits (7 units) * Management 6 credits (1 unit) 6 credits (1 unit) * Research project 12 credits (2 units) 12 credits (2 units) * Language work 6 credits (1 unit) 0 Among the Academic units there should be units equivalent to those taken by students on the Bath full-time MPhys course |

PHYS0045: Advanced topics
Semester 1
6
Credits: Contact:
Level: Undergraduate Masters
Assessment: EX80 CW20
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 two-yearly 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 School 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. |

PHYS0048: Introduction to quantum physics [NS]
Semester 1
6
Credits: Contact:
Level: Level 1
Assessment: EX70 CW20 PR10
Requisites: Co PHYS0049 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 wave-particle 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 - explain the origin of the periodic table. 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 alpha-particles and Rutherford's model. Photons and energy quantisation: Black-body radiation; the ultraviolet catastrophe and Plancks hypothesis. Photoelectric effect. The electromagnetic spectrum. X-rays. Compton scattering. Sources of photons; the Bohr model of the atom. Deficiencies of Bohr's model. Wave-particle duality: An introduction to waves. Wave-like 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 X-ray spectra. Shells, valency and chemical bonding. Students must have A-level Physics and A-level Mathematics in order to undertake this unit. Those students without A-level Mathematics must take MATH0103. |

PHYS0049: Relativity & astrophysics [NS]
Semester 2
6
Credits: Contact:
Level: Level 1
Assessment: EX70 CW20 PR10
Requisites: Co PHYS0048 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 large-scale structure - solve simple problems concerning orbital motion, blackbody radiation, cosmological redshift, stellar luminosity and magnitude. Content:Gravitation. Gravitational force and potential energy. Weight and mass. Circular orbits; Kepler's Laws; planetary motion. Escape velocity. Solar System. Earth-Moon system. Terrestrial planets; Jovian planets. Planetary atmospheres. Comets and meteoroids. Formation of the solar system. Stellar Evolution. Structure of the sun. Stellar distances, magnitudes, luminosities; black-body radiation; stellar classification; Hertzsprung-Russell diagram. The interstellar medium and star birth. Star death: white dwarfs, neutron stars, black holes. Galaxies. Galactic structure; classification of galaxies. Formation and evolution of galaxies. Active galactic nuclei and quasars. Astrophysical jets. Astrophysical Techniques. Telescopes and detectors. Invisible astronomy: X-rays, gamma-rays, cosmic rays, infrared and radio astronomy. Special Relativity. Galilean transformation. Speed of light - Michelson-Morley experiment; Einstein's postulates. Simultaneity; time dilation; space contraction; invariant intervals; rest frames; proper time; proper length. Causality. Lorentz transformation. Relativistic momentum, force, energy. Doppler effect. General Relativity. Gravity and geometry. The principle of equivalence. Deflection of light; curvature of space. Gravitational time dilation. Red shift. Black holes. The Universe. Large scale structure of the Universe. Hubble's Law. The expanding universe. The hot Big Bang. Cosmic background radiation and ripples therein. History of the universe. The missing mass problem. |

PHYS0050: Introduction to electronics [NS]
Semester 1
6
Credits: Contact:
Level: Level 1
Assessment: EX70 CW20 PR10
Requisites: Co PHYS0051, Ex PHYS0003 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 flip-flops - 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. Analysis of simple circuits using nodal voltage technique. Ideal voltage and current sources. Equivalent circuits. Thevenin's and Norton's theorems. Diodes. Ideal Operational Amplifiers: Theory of ideal operational amplifiers. Simple applications e.g. inverting and non-inverting amplifiers, addition and subtraction. Transients: Techniques for solving for transient waveforms in simple circuits involving inductors and capacitors. Initial conditions. 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. Bode plots. Combinational Logic: 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. PAL. Logic gates and characteristics: Basic implementation of gates using discrete devices (AND using resistors and diodes). Limitations. Logic family characteristics: Fan out, noise margin and propagation delay. Combinational functions: Adder, decoder, encoder, multiplexer, demultiplexer, ROM structure. Sequential logic: Latch, SR flip-flop and JK flip-flop. Shift register. Ripple and synchronous counters. Synchronous counter design. Basic RAM structure. Introduction to microprocessors (68000 based): Binary arithmetic. A simple microprocessor architecture and operation. Concepts of buses, input/output, DMA and interrupts. Students must have A-level Physics in order to undertake this unit. |

PHYS0051: Electricity & magnetism [NS]
Semester 2
6
Credits: Contact:
Level: Level 1
Assessment: EX70 CW20 PR10
Requisites: Co PHYS0050 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 forces and fields. Electric charge, Coulomb's Law, superposition of forces, electric charge distribution, the electric field, electric flux, Gauss's Law, examples of field distributions, dipole moment, energy of a system of charges. Electric potential. 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, conductors in an electric field, capacitors and their capacitance, energy stored. Magnetic fields. Magnetic force on a moving charge, definition of magnetic field, Lorentz force, force on a current carrying wire, force between current carrying wires, torque on a current loop. magnetic moment, Biot-Savart Law, Ampere's Law, magnetic flux, Gauss's Law, field in loops and coils. Electromagnetic Induction. Induced emf and examples, Faraday's Law, Lenz's Law, energy stored in a magnetic field, self and mutual inductance, energy stored in an inductor. Students must have A-level Physics in order to undertake this unit. |

PHYS0052: Properties of matter [NS]
Semester 1
6
Credits: Contact:
Level: Level 1
Assessment: EX70 PR10 CW20
Requisites: 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 Waal's model. The ideal solid - model potentials and equilibrium separations of molecules and Madelung crystals. Simple crystal structures, X-ray scattering and Bragg's law. First and second laws of thermodynamics, P-V-T 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 non-Newtonian) in liquids based on cage models. |

PHYS0053: Mechanics & waves [NS]
Semester 2
6
Credits: Contact:
Level: Level 1
Assessment: EX70 PR10 CW20
Requisites: 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 one-dimensional 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 one-dimensional structures - derive and apply the formulae for the non-relativistic 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 non-constant acceleration. Linear momentum, collisions, rockets. Work and Energy, potential energy, conservative and non-conservative 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 non-dispersive waves, phase and group velocity. Beats. Michelson interferometer. Doppler effect. |

PHYS0054: Quantum mechanics (distance learning)
Academic Year
12
Credits: Contact:
Level: Level 3
Assessment: EX
Requisites: Co PHYS0041 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 particle-wave 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 Schröödinger 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. Schrodingers equation: Operators for position, time, momentum and energy. Derivation of time-dependent Schrodinger equation. Correspondence to classical mechanics. Commutation relations and the Uncertainty Principle. Time evolution of states. Stationary states and the time-independent Schrodinger 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. Hydrogen-like 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. |

PHYS0055: Computational physics A
Semester 1
6
Credits: Contact:
Level: Level 3
Assessment: CW75 OR25
Requisites:
Pre PHYS0018Students should have taken an appropriate selection of year 1 and year 2 physics units, including PHYS0018 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 time-dependent quantum mechanical scattering, coupled oscillators, resonant phenomena, simple non-linear (including chaotic) systems, time-series analysis. Introduction to cellular automata, self-organisation and fractals. Applications to physical systems. Exercises and projects including interfacing to computer graphics. |

PHYS0056: Computational physics B
Semester 2
6
Credits: Contact:
Level: Level 3
Assessment: CW75 OR25
Requisites:
Pre PHYS0018,
Pre PHYS0031Aims & 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. |