Quantum Mechanics and Symmetry (QMS | SPA6325)

Year: 3 | Semester: B | Level: 6 | Credits: 15

Course organiser: Prof Steve Thomas | Course deputy: Dr Masaki Shigemori

Synopsis:

The course will give students a grounding in a more formal and axiomatic approach to quantum mechanics and introduce them to the application of these tools in the quantum mechanical description of symmetries in particle physics. Topics include: a mathematical introduction with basic notions on groups, Hilbert spaces, and linear operators; the formal axioms of quantum mechanics, Dirac notation; the free particle and the harmonic oscillator as the simplest quantum mechanical systems; time independent perturbation theory; multiparticle systems, identical particles; translations and rotations symmetries in quantum mechanics, conservation laws and good quantum numbers, representation of the ratation group, spin, addition of spin.

Aims:

The course to give students a general description of non-relativistic quantum mechanics in terms of Hilbert spaces and introduce the concept of spin and its relation to the representations of the rotation group.

Outcomes:

Students successfully completing this course will: understand what an abstract vector space is and how this concept underpins Quantum Mechanics in the form of the Hilbert space; be able to translate all they have previously learnt about quantum mechanics into this language; understand how quantum mechanical principles underly our picture of the sub-atomic and sub-nuclear world.

Recommended books:

Quantum mechanics
Cohen-Tannoudj, Diu, Laloe.
Wiley
ISBN: 0471569526
QM Library: QC174.1 COH

Modern quantum mechanics
J.J. Sakurai.
Addison Wesley
ISBN: 0201539292
QM Library: QC174.1 SAK

Quantum Mechanics Non-Relativistic Theory: Volume 3 L.D. Landau, E.M.
Lifshitz Butterworth-Heinemann
ISBN: 0750635398
QM Library: QC20 LAN/3

The Principles of Quantum Mechanics
P.A.M. Dirac
Clarendon Press
ISBN: 0198520115
QM Library: QC174.1 DIR