The third-year physics units listed here may not all be offered in any given year; students will be advised during enrolment as to which units are available in which semester. Physics units with insufficient enrolment may not be presented, and students will be advised as to appropriate alternatives. `Applications of quantum mechanics', `Solid state physics (crystallography)', `Statistical mechanics', and `Electromagnetism' are always offered in first semester while `Quantum mechanics', `Nuclear physics', `Solid state physics (lattice and electronic properties)' are always offered in second semester. The units are described below. Only prescribed texts are noted.
Applications of quantum mechanics
Synopsis Time-independant perturbation theory and application to Zeeman splitting, atomic polarisability of hydrogen. Degenerate perturbation theory. The variational approximation applied to the ground state of helium. Time-independant perturbation theory. Fermi's golden rule. Interaction of radiation and matter.
Prescribed texts
Mandl F Quantum mechanics Wiley, 1992
Classical field theory
Synopsis This is the same topic as is given in PHS4000 and may be taken in either third or fourth year. Variational principles for fields. Lagrangian formulation of classical fields. Energy-momentum tensors and conservation theorems. Hamiltonian formulation of the field equations. Canonical transformation theory for fields. Classical field theory. Introduction to the quantised Maxwell field.
Prescribed texts
Barut A O Electrodynamics and classical theory of fields and particles Dover, 1980
Complex analysis in physics
Synopsis Functions of a complex variable. Cauchy-Riemann equations. Homotopy theory. Multiply connected spaces. Cauchy's theorem. Contour integrals. Cauchy's integral formula. Taylor and Laurent expansions. Residues and poles. Energy spectrum; the complex E-plane. The residue theorem. Infinite integrals and series. Branch cuts, Riemann surfaces and topology. The Laplace and z transforms. Heaviside step function; the free propagator. The Hilbert transform. Analyticity and causality. Kramers-Kronig relations. Conformal mappings.
Computational physics
Synopsis This unit consists of eight laboratory sessions of six hours. Prior computing experience is not necessary. Assessment will be based on written reports for each session. Monte Carlo simulation of a 2-D Ising model. Phonons in a 1-D lattice. Trajectories in the Henon-Heiles potential. Structure of white dwarf stars. Hartree-Fock solutions of small atoms. Approximations to quantum scattering. Laplace's equation and viscous flow in 2-D. Time dependent Schrödinger equation. Optical ray tracing.
Electrical and optical properties
Synopsis As for MSC3011 (Materials science).
Electromagnetism
Synopsis Maxwell's equations, vector and scalar potentials, boundary equations. Plane electromagnetic waves in isotropic media. Cavity resonators. Transmission lines and effects of termination impedance. Waveguides, TE and TM modes in rectangular waveguides.
Prescribed texts
Cheng D K Field and wave electromagnetics Addison-Wesley, 1984
Elementary particles
Synopsis Quantum numbers including spin, parity, isotopic spin, strangeness and baryon/lepton number. Conservation laws of the fundamental interactions. Symmetry theories of multiplet structure.
Magnetic properties
Synopsis As for MSC3022 (Materials science).
Materials characterisation
Synopsis As for MSC3022 (Materials science).
Nuclear physics
Synopsis Topics chosen from the following. Review of binding energy, pairing and semi-empirical mass formula, mass parabolas. Characteristics of nuclear levels, shell model, spin-orbit coupling, level width. Interactions of radiation with matter, radiation detection. Radioactive decay, multipoles and gamma decay, selection rules. Beta decay and the neutrino. Fermi theory of beta decay. The nuclear force. The deuteron.
Prescribed texts
Krane W S Introduction to nuclear physics Wiley, 1987
Optics
Synopsis Scalar diffraction theory. Fresnel-Kirchhoff diffraction integral. Fraunhofer diffraction as the Fourier transform of an aperture transmission function. Fourier optics. Fresnel diffraction; concept of zones. Coherence; general interference law for partially coherent light. Laser principle; spontaneous and stimulated emission, amplification, threshold condition. Holography.
Order and chaos
Synopsis An introduction to the description of non-linear dynamical processes in various areas of physics, with emphasis on describing the phenomena and giving the simplest possible theoretical descriptions. Topics covered will include (i) the growth of ordered spatial structures out of fluctuating homogeneous states (Rayleigh-Benard convection, salt fingering, growth of precipitates from supersaturated solution); (ii) fractal growth processes such as diffusion-limited aggregation of colloidal particles; (iii) an introduction to dissipative chaotic phenomena as they occur in nature. Texts and references to be announced.
Quantum mechanics
Synopsis The aim is to discuss the underlying basic concepts of quantum mechanics and to apply the formalism to a number of physical problems, thereby illustrating approximation methods. The basic postulates of quantum mechanics. General properties of states and observables in the Schrödinger formulation. Matrix mechanics, basic sets, eigenvectors and secular equations. Commutation relations and angular momentum. Introduction of spin, Pauli spin matrices and spin wave functions. Pauli's exclusion principle and symmetry.
Prescribed texts
Mandl F Quantum mechanics Wiley, 1992
Relativity
Synopsis Tensor calculus in pseudo-Euclidean spaces. Lorentz transforms and applications to kinematics, dynamics and optics. Lorentz covariant matrices; world lines, proper time, 4-vectors for energy-momentum. Action principles and variational methods. Lagrangian and Hamiltonian formulations in relativity. Generalisation to include accelerating frames. Metric and Riemannian spaces. Eintstein's assumptions and their consequences.
Prescribed texts
Landau L D and Lifshitz E M Classical theory of fields, revised edn, Pergamon, 1982
Nayfeh M H and Brussel M K Electricity and magnetism, Wiley, 1985
Solid state physics (crystallography)
Synopsis This unit is not available to students who have taken MSC2011. Crystal structure and crystal symmetry, crystallographic rotation, applications of symmetry, diffraction of x-rays, electrons and neutrons by crystals, determination of crystal structure, defects in crystals.
Prescribed texts
Ashcroft N W and Mermin N D Solid state physics Holt, Rinehart and Winston, 1976
Solid state physics (lattice and electronic properties)
Synopsis Classification of crystalline solids and crystal bonding. Elastic properties of solids. The reciprocal lattice. Vibration of one-dimensional monatomic and diatomic lattices. Phonon dispersion curves and the measurement of anharmonicity. Classical theory of electrons in metals. Quantum theory for free electrons. Electronic properties of metals.
Prescribed texts
Ashcroft N W and Mermin N D Solid state physics Holt, Rinehart and Winston, 1976
Spectroscopy
Synopsis This is the same topic as is given in PHS4000 and may be taken in either third or fourth year. Transitions in quantised systems. Nuclear magnetic resonance and nuclear quadrupole resonance. Mössbauer spectroscopy. Electron spin resonance. Microwave, infrared and Raman spectroscopy. Electronic spectroscopy of atoms and molecules.
Statistical mechanics
Synopsis An introduction to how physical concepts such as heat, temperature and entropy can be understood from a microscopic, probabilistic viewpoint. The Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein probability distributions. Simple applications of the partition function will be treated.
Prescribed texts
Guenault A M Statistical physics Routledge, 1988
Stellar atmospheres
Synopsis Review of the observed properties of stars. Static stellar structure, radiative transport, the radiation field, opacity and emissivity, equation of radiative transfer, black body radiation, radiative equilibrium, true absorption and scattering. Radiation in the solar atmosphere, limb darkening, non-radiative energy transfer, Boltzmann and Saha equations, transition probabilities and line opacities, line broadening mechanisms, continuous opacity, simplified model of stellar atmospheres, line intensities in stellar spectra, curves of growth for stellar spectral lines.
Prescribed texts
Bohm-Vitasse E Introduction to stellar astrophysics Cambridge, volume 1-2, 1989
Symmetry methods
Synopsis Emphasis on symmetry methods for the solution of physical problems. Discrete and continuous groups. Group representations for the main groups in physics and chemistry. Generators and infinitesimal transformations for continuous groups. The rotation groups, SU(2) and permutation groups are covered in some detail. Assignments contain applications to classical electromagnetism, classical and quantum mechanics, optics, solid state physics and special relativity. Introduction to gauge symmetries and more advanced groups, such as SL(2,C).
Transform theory
Synopsis Bound and unbound functions, signal coherence and noise. Expansion of functions using basis sets. Reconstruction errors. Correlations and convolution; template matching; integration and summation of series. Fourier transforms in optics. The DFT; sampling and aliasing; Gibbs phenomenon; apertures and windows. Algorithms for the fast computation of transforms; the FFT; butterfly diagrams and bit-reversal algorithms. Number theoretic and prime factor transforms; Winograd transforms. Transforms such as DCT, Walsh, Haar etc. will also be examined.
Wave propagation
Synopsis Review of mathematical background: Fourier analysis, group and phase velocities, method of characteristics. Green's functions and integral solutions. The scalar wave equation and non-coherent optics: Kirchhoff solution, diffraction theory, Babinet's principle. The vector wave equation, solution of electromagnetic problems. Hertz potential and solutions for E and B, calculation of radiation fields, scattering from conducting spheres. Propagation in a scattering/absorbing medium. Diffusion and heat conduction, nature of the solutions, application to some time-dependent problems.
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