course-details-portlet

FY8104

Application of Symmetry Groups in Physics

Choose study year
Credits 7.5
Level Doctoral degree level
Course start Autumn 2025
Duration 1 semester
Language of instruction English and norwegian
Location Trondheim
Examination arrangement School exam

About

About the course

Course content

The course is given every other year, and will be given autumn 2025.

Transformations, generators, symmetries and conservation laws in quantum mechanics. Examples of groups. Conjugacy classes, subgroups, cosets, quotient groups, direct-product groups. Homomorphisms and isomorphisms. Representations and bases. Characters. Orthogonality relations and character tables for irreducible representations. Decomposition of reducible representations. Energy levels and degeneracy, perturbations and level splitting. Transfer and projection operators. Product representations. Continuous groups, Lie groups and Lie algebras. The rotation group and angular momentum. Irreducible tensor operators. Matrix elements and selection rules. Point groups. Space groups. Time reversal. Projective representations. Various applications, including crystal field splitting, optical spectra, and symmetry aspects of the band theory of crystals.

Learning outcome

The course gives an introduction to group theory that will make a student able to analyze symmetries and their implications in a systematic and unified way, including solving or simplifying various problems in atomic, molecular and solid state physics for which symmetry plays a role. The most important specific learning outcomes are

(i) to know the connection between the energy levels of a Hamiltonian operator and the irreducible representations of its symmetry group, and be able to determine how the energy levels are split by perturbations, e.g. the splitting of atomic energy levels in crystal fields, and

(ii) to be able to determine conditions for when matrix elements of irreducible tensor operators (including the Hamiltonian) can be nonzero (so-called selection rules), with applications to e.g. optical absorption spectra.

A more general learning outcome is that the unified discussion of symmetries will give a deeper understanding of the structure of quantum mechanics.

Learning methods and activities

Lectures and voluntary calculation exercises (in English and joint with FY3105).

Further on evaluation

The exam may be given in English only. The re-sit examination may be changed from written to oral.

Course materials

Information about relevant books will be given at the start of the course.

Credit reductions

Course code Reduction From
DIF4984 7.5 sp
FY3105 7.5 sp Autumn 2013
This course has academic overlap with the courses in the table above. If you take overlapping courses, you will receive a credit reduction in the course where you have the lowest grade. If the grades are the same, the reduction will be applied to the course completed most recently.

Subject areas

  • Physics

Contact information

Course coordinator

Department with academic responsibility

Department of Physics

Examination

Examination

Examination arrangement: School exam
Grade: Passed / Not Passed

Ordinary examination - Autumn 2025

School exam
Weighting 100/100 Examination aids Code C Date 2025-11-27 Time 15:00 Duration 4 hours Exam system Inspera Assessment
Place and room for school exam

The specified room can be changed and the final location will be ready no later than 3 days before the exam. You can find your room location on Studentweb.

Sluppenvegen 14
Room SL311 orange sone
4 candidates

Re-sit examination - Summer 2026

School exam
Weighting 100/100 Examination aids Code C Duration 4 hours Exam system Inspera Assessment Place and room Not specified yet.