Premium
Clebsch‐Gordan coefficients of symmetry groups
Author(s) -
van Den Broek P. M.,
Cornwell J. F.
Publication year - 1978
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220900123
Subject(s) - clebsch–gordan coefficients , eigenvalues and eigenvectors , orthonormal basis , orthonormality , mathematics , pure mathematics , unitary state , symmetry (geometry) , projection (relational algebra) , set (abstract data type) , matrix (chemical analysis) , space (punctuation) , group (periodic table) , algebra over a field , irreducible representation , physics , quantum mechanics , geometry , chemistry , law , computer science , algorithm , political science , chromatography , programming language , operating system
A method is given for the determination of Clebsch‐Gordan coefficients of finite groups. The Clebsch‐Gordan coefficients may be arranged into vectors which are eigenvectors of certain projection matrices. It is shown how an appropriate set of orthonormal eigenvectors of these matrices may be obtained; this set gives then a unitary matrix of Clebsch‐Gordan coefficients. The symmetry properties of these Clebsch‐Gordan coefficients are studied with special emphasis on the crystallographic space groups.