PH5003
Group Theory
2019-2020
15
7
SCQF level 11
Both
Academic year(s): 2019-2020
SCOTCAT credits : 15
ECTS credits : 7
Level : SCQF level 11
Semester: Both
Availability restrictions: Normally only taken in the final year of an MPhys or MSci programme involving the School
Planned timetable:
This module explores the concept of a group, including groups of coordinate transformations in three-dimensional Euclidean space; the invariance group of the Hamiltonian operator; the structure of groups: subgroups, classes, cosets, factor groups, isomorphisms and homorphisms, direct product groups; introduction to Lie groups, including notions of connectedness, compactness, and invariant integration; representation theory of groups, including similarity transformations, unitary representations, irreducible representations, characters, direct product representations, and the Wigner-Eckart theorem; applications to quantum mechanics, including calculation of energy eigenvalues and selection rules.
Pre-requisite(s): Before taking this module you must ( pass PH2011 and pass PH2012 ) and pass MT2001 or ( pass MT2501 and pass MT2503 ) and pass PH3081 or pass PH3082 or ( pass MT2506 and pass MT2507 ) and pass PH3061 and pass PH3062. Pre-requisites are compulsory unless you are on a taught postgraduate programme.
Weekly contact: 3 lectures or tutorials.
Scheduled learning hours: 32
Guided independent study hours: 118
As used by St Andrews: 2-hour Written Examination = 100%
As defined by QAA
Written examinations : 100%
Practical examinations : 0%
Coursework: 0%
Re-assessment: Oral Re-assessment, capped at grade 7
Module coordinator: Professor J F Cornwell
Module teaching staff: Prof J Cornwell
Most physical systems possess some symmetry. In some cases these are geometrically obvious. For example atoms have spherical symmetry and crystals have both translational and rotational symmetry. However, in other situations, such as in the theory of fundamental particles (quarks, gluons, etc), symmetry concepts are still very vital even though they may not be intuitively obvious geometrically. Group Theory provides a systematic way of dealing with all the types of symmetry that appear in physics, and extracting the maximum amount of information that results from the symmetry.
Aims & Objectives
To present all the necessary ideas on group theory and show how they can be applied to the quantum mechanical study of physical problems that possess symmetry.
Learning Outcomes
By the end of the module, the students should have a good knowledge of the topics covered in the lectures, and should:
Synopsis
An introductory survey, involving: the definition of a group, with physically important examples, a detailed treatment of rotations and translations, the connection with quantum mechanics, the basic concepts of `abstract' group theory (subgroups, classes, cosets, factor groups, homomorphic and isomorphic mappings, direct product groups, etc), for which no previous knowledge is assumed, basic ideas of the theory of Lie groups, starting with a definition, and including the concepts of connectedness, compactness, and invariant integration, theory of matrix representations of groups, including the ideas of equivalent representations, reducible and irreducible representations, unitary representations, characters, projection operators for determining basis functions, direct-product representations, irreducible tensor operators, and the Wigner-Eckart theorem, applications to quantum mechanics, including solving the Schrodinger equation, determining selection rules and transition probabilities. Pre-requisites - some previous knowledge of quantum mechanics, including perturbation theory; some knowledge of matrices; no previous knowledge of group theory is assumed.
Recommended Books
Please view University online record:
http://resourcelists.st-andrews.ac.uk/modules/ph5003.html
General Information
Please also read the general information in the School's honours handbook that is available via st-andrews.ac.uk/physics/staff_students/timetables.php.