Group Theory in Crystal Physics

  • H. Jones
Part of the Optical Physics and Engineering book series (OPEG)


Group theory is used in crystal physics to obtain a classification of electronic states and of normal modes of lattice vibrations. In one important application it is used to determine all possible symmetries of the wave functions of a single electron in a given space-periodic field. Another application consists of the determination of the symmetries of the states of an impurity atom subject to a field imposed by the neighboring atoms of crystal. The same theory applies in a very similar form to the analogous situation of lattice vibrations, either in a perfect lattice or in a lattice containing impurity atoms.


Irreducible Representation Brillouin Zone Point Group Reciprocal Lattice Diagonal Form 


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  1. 1.
    A. Speiser, Theorie der Gruppen von Endlicher Ordnung, Springer-Verlag (Berlin), 1937.Google Scholar
  2. 2.
    Allen Nussbaum, Solid State Phys. 18: 165 (1966).CrossRefGoogle Scholar
  3. 3.
    H. Jones, Theory of Brillouin Zones and Elecronic States in Crystals, North-Holland Publishing Co. ( Amsterdam ), 1960.Google Scholar

Copyright information

© Springer Science+Business Media New York 1969

Authors and Affiliations

  • H. Jones
    • 1
  1. 1.Department of MathematicsImperial CollegeLondonEngland

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