F8190 Application of groups to the theory of solids

Faculty of Science
Spring 2027
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
Jan Kuneš, Ph.D. (lecturer)
Guaranteed by
Jan Kuneš, Ph.D.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: Jan Kuneš, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Prerequisites
F5030 Intro. to Quantum Mechananics && F1110 Linear algebra and geometry
basics of quantum mechanics linear algebra
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Abstract
Understanding the concepts of symmetry, group, and group representation. Understanding the concept of an irreducible representation. Ability to apply representation theory to various aspects of quantum theory of materials, e.g., state degeneracies, selection rules, the form of the Hamiltonian for a given symmetry. Mastery of working with representation tables of point groups.
Key topics
  • Motivation: What are symmetry operations, and why are they fundamental tools for a physicist?
  • Definition of a group and its associated structures (subgroup, class, etc.).
  • Representation of a group in a linear vector space. Irreducible representations. Schur’s lemmas.
  • Character of a representation. Character tables.
  • Basis functions.
  • Applications: Crystal field, selection rules.
  • Permutation group, many-electron functions. Tanabe-Sugano diagrams.
  • Spin and spin-orbit coupling. Double groups.
Study resources and literature
  • DRESSELHAUS, M. S.; G. DRESSELHAUS and A. JORIO. Group theory : application to the physics of condensed matter. Berlin: Springer-Verlag, 2008, xv, 582. ISBN 9783540328971. info
Approaches, practices, and methods used in teaching
lectures, homework
Method of verifying learning outcomes and course completion requirements
oral exam
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught every week.
General note: S.
The course is also listed under the following terms Spring 2025.
  • Enrolment Statistics (Spring 2027, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2027/F8190