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Bases for the irreducible representations of O(3) symmetry adapted to a crystallographic point group
Author(s) -
Gould M. D.,
Chandler G. S.
Publication year - 1987
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560310323
Subject(s) - irreducible representation , point group , angular momentum , symmetry (geometry) , group (periodic table) , symmetry group , point (geometry) , mathematics , rotation group so , clebsch–gordan coefficients , physics , mathematical physics , combinatorics , pure mathematics , quantum mechanics , geometry
We construct bases for the irreducible representations of the rotation group O (3) which are symmetry adapted to a Crystallographic point group. We obtain explicit expressions for the cubic groups, which are valid for arbitrary values of the angular momentum quantum number l . Our method yields an efficient algorithm for both analytical and numerical work. An explicit formula for the multiplicities of an irreducible representation for the cubic groups in an arbitrary angular momentum term l is also derived.