Advanced Quantum Mechanics
|Unit level:||Level 4|
|Teaching period(s):||Semester 2|
|Offered by||School of Physics and Astronomy|
|Available as a free choice unit?:||N
- PHYS20401 - Lagrangian Dynamics (Recommended)
To deepen understanding of Quantum Mechanics.
To prepare students for courses in quantum field theory and gauge theory.
On completion successful students will be able to:
1. find the unitary transformations linked to symmetry operations.
2. apply time-dependent perturbation theory to variety of problems.
3. derive a mathematical description of quantum motion in electromagnetic fields.
4. apply the relativistic wave equations to simple single-particle problems.
- Written exam - 100%
1. Symmetries in quantum mechanics (5 lectures)
Unitary operators - translations in space and translations in time (evolution)
Rotations, reflections and parity
Schrödinger vs Heisenberg picture
2. Time-dependent perturbation theory (5 lectures)
Fermi's Golden Rule
Selection rules for atomic transitions
Emission and absorption of radiation
Finite width of excited state
Selection rules for hydrogen
3. Coupling to E&M fields (4 lectures)
Minimal coupling, Landau levels, gauge invariance of QM
4. Relativistic wave equations (8 lectures)
The Klein-Gordon equation and Dirac equations and their solutions
Chirality and helicity
Lorentz invariance and the non-relativistic limit
The hydrogen atom and fine structure
There is no single book that covers all the material in the course. The following books represent a basic choice; a longer list will be discussed at the first lecture.
Shankar R., Principles of Quantum Mechanics 2nd ed, 3rd printing (Springer, 2008)
Atkinson I.J.R. and Hey, A.J.G. Gauge Theories in Particle Physics, Vol 1 (IoP, 2003)
Feedback will be available on students’ individual written solutions to examples sheets, which will be marked when handed in. Model answers will be issued.
- Assessment written exam - 1.5 hours
- Lectures - 24 hours
- Independent study hours - 74.5 hours