Representations of Continuous and Point Groups
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.
KeywordsSymmetry Group Irreducible Representation Conjugacy Class Point Group Rotation Group
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