Lecture Units

The following lecture units may be offered in 2005:

  • The "core units" A - D are normally compulsory for all students.
  • Units A, C and D will be given in Session 1 and unit B will be given in Session 2.
  • The elective units E - H can only be offered if there is sufficient demand and for this reason you will be asked for your preferences before Session 2.
  • Students should take 2 elective units in addition to the 4 core units. It is sometimes possible to substitute other courses for some of those in the above list, for example Honours units from other Schools. Advice should be sought from the Undergraduate Director.
  • Brief syllabi for the various lecture units are given in the following pages. Further details will be supplied by the lecturers concerned and can be obtained upon request. Note that the core units A - D assume knowledge of the material covered in the corresponding Level III units given in the School.

Writing your Honours Theses:

The theses will require a statement clearly stating what actual work the student has performed. You are advised to discuss this statement with your supervisor.

In marking your report assessors will take into account the following aspects:

  1. Literature review
  2. Understanding of principles
  3. Clarity of expression
  4. Orderliness
  5. Soundness of arguments
  6. Techniques (experimental and theoretical)
  7. Presentation of results
  8. Suggestions for further work, etc 

See Writing an Honours Thesis for further guidelines.  

Unit A: QUANTUM MECHANICS See also Lecture Notes

PART 1

1) Systems of identical particles, fermions and bosons. Pauli exclusion principle for fermions. Helium atom. Exchange interaction. Multielectron atoms and periodic table.

2) Diatomic molecules and molecular binding. Molecular orbitals. The simplest molecule H2+, Born-Oppenheimer approximation, electronic, vibrational and rotational spectra of diatomic molecules.

3) Charged particle in an external magnetic field. Gauge invariance. Landau levels.

4) Heisenberg formulation of quantum mechanics. Example: 1D harmonic oscillator, creation and annihilation operators.

PART 2

Relativistic equations: Klein-Gordon equation, Dirac equation.

Scattering Theory: Scattering amplitude, Born approximation, Low-energy scattering, scattering phases, resonance scattering.


Unit B: STATISTICAL MECHANICS

1. Classical Gases and Liquids

Cluster expansion and virial coefficients for imperfect gas; introduction to theories of liquids; distribution functions; the HNC and PY approximations; molecular dynamics simulations; Debye-Hückel theory of electrolytes.

2. Phase Transitions and Critical Phenomena

Phenomenology of first and second order phase transitions; critical points and critical exponents; Landau theory; the Ising model and applications, approximate and exact solutions; percolation problems.

3. Approach to Equilibrium, Transport Phenomena, and Irreversibility

Boltzmann transport equation, approximate solutions; the H theorem and the problem of irreversibility; Liouville equation, time correlation functions, Linear response theory; Brownian motion; Boltzmann's ergodic hypothesis, Gibbs mixing, Birkoff's theorem, the baker's map.

 

Unit C: SOLID STATE PHYSICS

1. Band Theory

Electrons in periodic solids; nearly-free-electron approximation; tight-binding method,

s-electrons in cubic lattices; Density Functional approaches.

2. Electron Dynamics

The Fermi surface; effective mass; energy levels and orbits in a magnetic field; cyclotron resonance; de Haas-van Alphen effect; examples from real materials.

3. Fundamentals of Magnetism:

Origins of magnetism, Hund's rules; exchange interaction,
diamagnetism, paramagnetism, Curie law, molecular field, Curie-Weiss law

4. Magnetic Structures

Magnetic ordering, ferromagnetism and antiferromagnetism;
anisotropy, domains, neutron scattering determination of magnetic
structures.

 

Unit D: ELECTROMAGNETISM and THE STANDARD MODEL

2003 Exam Questions

1. Electrodynamics
a. Relativistic notation, 4-vectors,
2. Vector potential, tensor of EM field,
3. Gauge invariance,
4. Action of a particle in an EM field and action of an EM field,
5. Lagrangian
6. Equations of motion – Maxwell’s equations, and equation for a charged
particle (Examples: electron in static electric or/and magnetic fields,
electron in an electromagnetic wave).
7. Liénard - Wiechert retarded potentials and fields,
8. Radiation from an accelerated particle:
 a. synchrotron radiation, spectrum, polarization and angular distribution
b. dipole radiation (reminder)
9. Scattering of EM waves
a. long-wave limit
b. short wave limit
10. Dirac monopoles, quantization condition, dyons

Unit E: ADVANCED CONDENSED MATTER PHYSICS

1. Semiconductors

Tunnelling and barriers; low dimensional semiconductor systems; reduced size and dimensionality effects; density of states; quantum Hall effects; electronic transport in mesoscopic systems.

2. Superconductors

BCS theory: Ginzburg-Landau theory; flux quantisation, vortices, Type-II superconductors, Josephson effect; high temperature superconductivity 

3. Magnetism

Spin waves; low temperature thermodynamics of magnetic systems; systems with RKKY interactions; mean field theory of itinerant electron magnetism; incommensurability; frustration and spin glasses.

 

Unit F: These two courses are offered in alternate years

ASTROPHYSICS

1. The Interstellar Medium and the Physics of Gaseous Nebulae

The Interstellar Medium; Radiative Transfer; local thermodynamic equilibrium; ionization and recombination; emission lines; dynamics; shock waves; HII regions; Supernova remnants.

2. Selected Topics in Cosmology

The expanding Universe; Newtonian Cosmology; the cosmological parameters; problems with the standard Big Bang; inflation, cosmic microwave background radiation.

or

COSMOLOGY AND THE INTERSTELLAR MEDIUM

This course describes the observations and physics of the interstellar medium. We will look at the variety of phases in the interstellar medium and gain an understanding of the observations that reveal its structure. We will also investigate the physical processes that enable this multiphase structure to be maintained. This course explores the basics of modern cosmology. We will investigate some of the observations which have led to the construction of the Big Bang Theory of the evolution of the universe.

 

Unit G: QUANTUM FIELD THEORY

1. Relativistic Wave Equations

The Klein-Gordon and Dirac equations; momentum space expansions; current conservation; Lorentz covariance; hole theory.

2. Canonical Lagrangian Field Theory

Classical quantization; canonical quantization for fields; symmetries and conservation laws.

The Klein-Gordon, Dirac and electromagnetic fields. Equations of motion; commutation relations; Feynman propagators.

3. Quantum Electrodynamics

Perturbation theory; Wick's theorem; the S-matrix expansion; trace calculations. Applications to Coulomb scattering, Compton scattering, etc. Higher-order processes: vacuum polarization, electron self-mass, vertex corrections. Renormalization.

4. Introduction to Gauge Theories

Gauge invariance; Yang-Mills theory; spontaneous symmetry breaking; the Goldstone and Higgs mechanisms; unification of the weak and electromagnetic interaction; quantum chromodynamics.

Unit H: Atomic & Molecular Physics

Atomic Physics

One-electron atoms (revision), multi-electron atoms, atomic units., Hartree-Fock, self consistent field, Slater determinant, atomic shells, relativistic effects, spin-orbit interaction, Hund's rule, electromagnetic transitions, selection rules, atomic spectroscopy.

Diatomic Molecules

Born-Oppenheimer approximation, hydrogen molecule, valence bond treatment of hydrogen molecule, Coulomb and exchange, spin, molecular orbital treatment of H2+.

Polyatomic Molecules

Molecular symmetry, symmetry groups, matrix representations, symmetry species, character tables, degeneracy, molecular orbitals, buildup, LCAO's, polyatomic molecules, methods for calculating molecular orbitals of polyatomic molecules, examples: H2O, N, practical methods, density functional theory, electron correlation.

Molecular Spectroscopy

Energies, selection rules, electronic transitions, molecular vibrations, infrared, optical and Raman spectroscopy, examples.

Special Topics

Some applications of molecular physics. Depending on the lecturer this might include macromolecules, polymers, biological applications, atmospheric physics, remote sensing.


Further Information

For more information about the Honours Year contact:

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