Lecture Units

The following lecture units may be offered in 2010:

  • 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.
  • 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. (PHYS3210 Quantum Mechanics; PHYS3020 Statistical Physics; PHYS3230 Electromagnetism; and PHYS3080 Solid State Physics)

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. Interaction in classical fluids

Cluster expansions for an imperfect gas; the product theorem; Ursell cluster functions, articulation and nodal circles; introduction to theories of liquids; distribution functions; Orstein Zernike equations; the HNC and PY approximations; the virial expansion and equations of state; comparison with molecular dynamics simulations;

2. Phase Transitions and Critical Phenomena

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

3. Approach to Equilibrium, Transport Phenomena, and Irreversibility

Brownian motion; Boltzmann transport equation, approximate solutions; the H theorem and the problem of irreversibility; Liouville equation, time correlation functions, Linear response theory; The fluctuation theorem.

 

Unit C: SOLID STATE PHYSICS Lecture Notes

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 (offered in even years)

or

COSMOLOGY AND THE INTERSTELLAR MEDIUM (offered in odd years)

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

The aim is to make Quantum Field Theory (QFT) clear, informative and interesting for all.

Speaking simply QFT is a branch of physics, which studies general properties, which describe the behaviour of Bose and Fermi particles in different situations. This means different types of interactions between them, different external conditions etc. The subject of QFT is diverse and the just given simple definition does not cover every aspect of it, but it suffices for our needs.

The purpose of this course is to provide an introduction to the subject in such a way that it can be useful and interesting for students who are going to pursue a career in any field of physics, for example  in atomic physics, astrophysics, condense matter physics etc. For those few students who would intend to undertake research in high energy physics this course may serve as a first, preliminary encounter with their area of interests.

The subject is introduced by addressing several phenomena, including the following ones:

  • Casimir effect
  • Lamb shift - splitting of atomic energy levels, which from the first glance should be degenerate
  • Vacuum polarization
  • Heizenerg-Euler problem, behaviour of the vacuum in strong magnetic field
  • Schwinger phenomenon, production of electron - positron pairs in static electric field

Their general properties as well as relations with phenomena that take place at low energies (say, in atomic and condensed matter physics, or astrophysics) are outlined. The physical content is made the centre point of the discussion while the necessary theoretical formalism is reduced to the minimum and reformulated in most simple terms, which are accessible and, hopefully, attractive for any honours student.

 

Unit H: Atomic & Molecular Physics (not offered in 2010)

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:

    last updated Feb 1 2011