# MMath&Phys Mathematics and Physics / Course details

Year of entry: 2024

## Course unit details:Advanced Quantum Mechanics

Unit code PHYS40202 10 Level 4 Semester 2 No

### Pre/co-requisites

Unit title Unit code Requirement type Description
Lagrangian Dynamics PHYS20401 Pre-Requisite Recommended
Mathematical Fundamentals of Quantum Mechanics PHYS30201 Pre-Requisite Compulsory
Electrodynamics (M) PHYS30441 Pre-Requisite Compulsory

PHYS40481 - Quantum Field Theory

PHYS40682 - Gauge Theories

### Aims

1. To  enhance knowledge and understanding of Quantum Mechanics.

2. To prepare students for Quantum Field Theory, Gauge Theories and other related courses.

### 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.

### Syllabus

1.    Symmetries in quantum mechanics

Rotations, space-time reflections and parity

Unitary operators for space and time translations

Conversation laws

Schrödinger vs Heisenberg picture

2.    Time-dependent perturbation theory

Fermi's Golden Rule

Selection rules for atomic transitions

Finite width of excited state

Selection rules for hydrogen

3.    Coupling to E&M fields

Minimal coupling

Landau levels

The Gauge Principle in Quantum Mechanics

The Pauli-Schrödinger equation

4.     Relativistic wave equations

The Klein-Gordon equation

The Dirac equations

Chirality and helicity

Lorentz invariance and the non-relativistic limit

The hydrogen atom and fine structure

Graphene

### Assessment methods

Method Weight
Written exam 100%

### Feedback methods

Feedback will be provided via solutions to the problem sheets, which will be made available electronically on Blackboard. More detailed feedback will be provided through examples classes which are integrated within the 24 lectures.

There is no single book that covers all the material in the course. The following books represent a basic choice:

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)

### Study hours

Scheduled activity hours
Assessment written exam 1.5
Lectures 24
Independent study hours
Independent study 74.5

### Teaching staff

Staff member Role
Ahsan Nazir Unit coordinator