FY8104 - Application of Symmetry Groups in Physics


Examination arrangement

Examination arrangement: Work
Grade: Letters
Term:  Autumn

Evaluation Weighting Duration Grade deviation Examination aids
Work 100/100

Examination arrangement

Examination arrangement: School exam
Grade: Passed/Failed
Term:  Spring

Evaluation Weighting Duration Grade deviation Examination aids
School exam 100/100 4 hours C

Course content

The course is given every other year, next time autumn 2021. 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 To
DIF4984 7.5
FY3105 7.5 AUTUMN 2013
More on the course



Version: 1
Credits:  7.5 SP
Study level: Doctoral degree level


Term no.: 1
Teaching semester:  AUTUMN 2021

Language of instruction: English, Norwegian

Location: Trondheim

Subject area(s)
  • Physics
Contact information
Course coordinator:

Department with academic responsibility
Department of Physics


Examination arrangement: Work

Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
Autumn ORD Work 100/100





Room Building Number of candidates

Examination arrangement: School exam

Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
Spring ORD School exam 100/100 C INSPERA
Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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