
AMA4001 Advanced Quantum Theory (1^{st} semester)
Prerequisite: AMA3002 or, subject to the approval of HoT PHY3011
Introduction
The course is intended as a follow on from AMA3002 Quantum Theory.
Contents
1) Review of fundamental quantum theory (Postulates of quantum mechanics; Dirac notation; Schrödinger equation; spin1/2 systems; stationary perturbation theory).
2) Particle in a central potential. Hydrogen atom.
3) Coupled angular momenta: spin1/2 coupling; singlet and triplet subspaces for two coupled spin1/2 particles; Coupling of general angular momenta;
4) Spinorbit coupling and the fine structure of the hydrogen atom.
5) Timedependent perturbation theory.
6) Elements of collisions and scattering in quantum mechanics.
7) Identical particles and second quantisation; operators representation.
8) Basics of electromagnetic field quantisation.
9) Systems of interacting bosons.
Learning Outcomes
On successful completion of the module, it is intended that students will be able to:
1) Understand the physics of particles in a central potential with special emphasis on hydrogenlike systems.
2) Use the rules for the construction of a casis for coupled angular momenta.
3) Grasp the fundamental features of the fine structure of the hydrogen atom.
4) Understand the techniques for dealing with timedependent perturbation theory.
5) Apply the theory of scattering to simple quantum mechanical problems.
6) Describe systems of identical particles in quantum mechanics and write the second quantisation representation of operators.
7) Apply the formalism of second quantisation to the electromagnetic field and systems of interacting bosons.
Assessment
Exam 80% Presentation 20%
Textbooks/Other Materials
Quantum Physics, 3rd ed., by Gasiorowicz, library shelfmark: QC174.12 GASI
The Physics of Quantum Mechanics, by Binney and Skinner
Quantum Mechanics, 2nd ed., by Bransden and Joachain, shelfmark QC174.12 BRAN
Principles of Quantum Mechanics, 2nd ed., by Shankar
Quantum Mechanics (Nonrelativistic theory), by Landau and Lifshitz, shelfmark QC174.1 LAND
Introduction to Quantum Mechanics, by David J. Griffiths, Ch.11 for Scattering Theory
Advanced Quantum Mechanics, by Franz Schwabl, for second quantisation. Library shelfmark: QC174.12 SCHW