Advanced Quantum Theory

Overview

1. Review of fundamental quantum theory (Postulates of quantum mechanics; Dirac notation; Schrödinger equation; spin-1/2 systems; stationary perturbation theory).
2. Coupled angular momenta: spin-1/2 coupling; singlet and triplet subspaces for two coupled spin-1/2 particles; Coupling of general angular momenta;
3. Spin-orbit coupling; fine and hyperfine structures of the hydrogen atom.
4. Time-dependent perturbation theory.
5. Elements of collisions and scattering in quantum mechanics.
6. Identical particles and second quantisation; operators representation.
7. Basics of electromagnetic field quantisation.
8. Systems of interacting bosons: Bose-Einstein condensation and superfluidity.

Learning Objectives

On successful completion of the module, it is intended that students will be able to:
1. Use the rules for the construction of a basis for coupled angular momenta.
2. Grasp the fundamental features of the fine and hyperfine structures of the hydrogen atom.
3. Understand the techniques for dealing with time-dependent perturbation theory.
4. Apply the theory of scattering to simple quantum mechanical problems.
5. Describe systems of identical particles in quantum mechanics and write the second quantisation representation of operators.
6. Apply the formalism of second quantisation to the electromagnetic field and systems of interacting bosons.

Skills

Mathematical modelling. Problem solving. Abstract thinking.

Assessment

None