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Clebsch–Gordan coefficients for chains of groups of interest in quantum chemistry. III. The point symmetry groups
Author(s) -
Kibler M. R.
Publication year - 1983
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.560230113
Subject(s) - clebsch–gordan coefficients , symmetry (geometry) , group (periodic table) , connection (principal bundle) , point group , series (stratigraphy) , molecular symmetry , mathematical physics , chemistry , point (geometry) , chain (unit) , group theory , quantum , nonlinear system , symmetry group , quantum mechanics , physics , pure mathematics , mathematics , irreducible representation , combinatorics , molecule , geometry , paleontology , biology
This work amalgamates some basic elements defined in the first paper of this series and in related papers with the theory of coupling coefficients for an arbitrary group with the view of generating the Clebsch–Gordan coefficients and V symbols for point symmetry groups. The connection between Clebsch–Gordan coefficients and V symbols is established for an arbitrary group in a form that reduces to the one known for the chain SU (2) ⊃ U (1). The Clebsch–Gordan coefficients and V symbols of any point symmetry group G are shown to be obtainable from Clebsch–Gordan coefficients and \documentclass{article}\pagestyle{empty}\begin{document}$ {\bar f} $\end{document} symbols of the chain SU (2) ⊃ G through the resolving of a system of nonlinear equations.