## PH10132: Core physics

[Page last updated: 23 October 2023]

Owning Department/School: Department of Physics
Credits: 12 [equivalent to 24 CATS credits]
Notional Study Hours: 240
Level: Certificate (FHEQ level 4)
Period:
Assessment Summary: EXCB 50%, EXOB 50%
Assessment Detail:
• PH12031 MCQ examination 1 (EXCB 25%)
• PH12031 MCQ examination 2 (EXCB 25%)
• PH12031 Written examination (EXOB 50%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: You must have A-level Physics (or equivalent) to take this module
Learning Outcomes: After taking this unit the student should be able to:
• apply the wavefunction for a one-dimensional travelling wave to problems involving mechanical, acoustic, water and electromagnetic waves;
• describe models of the atom, the origin of quantisation of energy and the origin of the periodic table;
• show how quantisation arises from boundary conditions and calculate energy levels in simple model systems;
• construct ray diagrams for use in solving simple geometrical optics problems;
• outline the mathematical analysis of multiple-beam interference.

Content: You will advance your knowledge and understanding of some fundamental areas of Physics, particularly quantum mechanics, vibrations, waves and optics.

Content: Vibrations and waves (11 lecture hours): Simple harmonic motion: Oscillations, including damped and forced oscillations. Resonance, Q-factors. Coupled oscillations and introduction to normal modes. Wave motion as the limit of coupled oscillations. The wave equation (1D). Introduction to waves: Transverse and longitudinal waves. Plane, circular and spherical waves. Waves on strings; sound, water, particle and light waves. Mathematical representation of 1D plane waves; wavefunction, amplitude, frequency, wavelength, wavenumber, speed, energy, intensity and impedance. The Doppler effect. Superposition; standing waves, beats, interference. Phase and group velocity; dispersive and non-dispersive media. Complex exponential notation. Mechanical impedance. Reflection and transmission at boundaries.

Quantum mechanics in 1D (15 lecture hours): Motivation: evidence for QM, Planck's quantum hypothesis, wave-particle duality, de Broglie & Planck-Einstein relations, uncertainty principle. Wave mechanics: Wave functions, probability density and normalisation. Observables; position, momentum and energy. Schrödinger's equation; time dependence of the wavefunction, stationary states, superposition and measurement, time-independent Schrödinger equation. Motion in one dimension: Eigenfunctions of the infinite square well, parity of solutions, superposition states. Dirac notation. Bound states of the finite square well. Motion of free particles. Reflection and transmission at a step. Tunnelling through a barrier. The harmonic oscillator.

Optics (10 lecture hours): The propagation of light: Optical path length. Huygen's and Fermat's principles, Snell's Law. Reflection and refraction. Lenses; the focal plane. Geometric optics for thin lenses. Aberrations. Principles of the telescope and microscope. Interference and diffraction: Coherence. Young's slits experiment. The Michelson interferometer. The Fabry-Perot etalon. Interference between N equally spaced sources. Fraunhofer diffraction as far-field case. Derivation of Fraunhofer pattern for single slit. Discussion of circular aperture, diffraction limits on optical systems, definition of resolution, Rayleigh criterion. The diffraction grating. Resolving power of the telescope and grating.

Course availability:

#### PH10132 is Optional on the following courses:

Department of Mathematical Sciences
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 2)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 2)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 2)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 2)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 2)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 2)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 2)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 2)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 2)

 Notes: This unit catalogue is applicable for the 2023/24 academic year only. Students continuing their studies into 2024/25 and beyond should not assume that this unit will be available in future years in the format displayed here for 2023/24. Courses and units are subject to change in accordance with normal University procedures. Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules. Find out more about these and other important University terms and conditions here.