Representations of Continuous and Point Groups

  • Laurent-Patrick Lévy
Part of the Texts and Monographs in Physics book series (TMP)


This appendix gives only the minimal requirements for using representations of symmetry groups in solid state physics. Many text books deal with this subject in greater detail and some are given in the Bibliography. Physical systems are often invariant under certain symmetry operations forming a group G. For example, electrons in an atom are subject to a central potential which is invariant under the group of rotations. Likewise, electrons in a solid are in a periodic potential which has translational invariance, but is also invariant under the point group of the lattice. There are 32 point symmetry groups in three dimensions, compatible with translational invariance of a crystal lattice. Wave functions corresponding to stationary solutions of the Schrödinger equation form a vector space, or state space.


Symmetry Group Irreducible Representation Conjugacy Class Point Group Rotation Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 572.
    Hammermesh, M. (1964) Group Theory and its Application to Physical Problems. Addison-WesleyGoogle Scholar
  2. 573.
    Serre, J.P. (1967) Representation lineaire des groupes finis. Hermann, ParisGoogle Scholar
  3. 574.
    Wigner, E.P. (1959) Group Theory and its Application to the Quantum Mechanics of Atomic Spectra. Academic PressMATHGoogle Scholar
  4. 575.
    Pikus, G.E., Bir, G.L. (1974) Symmetry and Strain Effects in Semiconductors. Wiley, New YorkGoogle Scholar
  5. 576.
    Schläfer, H.L. (1967) Einfürung in die Ligandenfeldtheorie. Akademische Verlaganstalt, FrankfurtGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Laurent-Patrick Lévy
    • 1
  1. 1.MPI für Festkörperforschung, Laboratoire des Champs Magnétiques IntensesCNRSGrenoble Cedex 9France

Personalised recommendations