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Advanced Quantum Mechanics

Unit code: PHYS40202
Credit Rating: 10
Unit level: Level 4
Teaching period(s): Semester 2
Offered by School of Physics and Astronomy
Available as a free choice unit?: N





To deepen understanding of Quantum Mechanics.

To prepare students for courses in quantum field theory and gauge theory.

Learning outcomes


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. 

Assessment methods

  • Written exam - 100%



1.    Symmetries in quantum mechanics (5 lectures)


Unitary operators - translations in space and translations in time (evolution)

Rotations, reflections and parity

Conversation laws

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

Pauli-Schrödinger equation


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


Recommended reading


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 methods


Feedback will be available on students’ individual written solutions to examples sheets, which will be marked when handed in. Model answers will be issued.


Study hours

  • Assessment written exam - 1.5 hours
  • Lectures - 24 hours
  • Independent study hours - 74.5 hours

Teaching staff

Yang Xian - Unit coordinator

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