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Symmetrization of eigenfunctions of angular momentum in point groups
Author(s) -
Li An Yong,
Liao Mu Zhen
Publication year - 2001
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.1059
Subject(s) - angular momentum , eigenfunction , basis (linear algebra) , mathematics , eigenvalues and eigenvectors , clebsch–gordan coefficients , point group , angular momentum operator , point (geometry) , group (periodic table) , irreducible representation , total angular momentum quantum number , angular momentum coupling , operator (biology) , projection (relational algebra) , mathematical physics , mathematical analysis , hermitian matrix , matrix (chemical analysis) , symmetry (geometry) , physics , quantum mechanics , pure mathematics , geometry , biochemistry , chemistry , materials science , repressor , algorithm , composite material , transcription factor , gene
Abstract The eigenfunctions | jm 〉 of angular momentum can combine linearly to make basis functions of irreducible representations of point groups. We surmount the projection operator and find a new method to calculate the combination coefficients. It is proven that these coefficients are components of eigenvectors of some hermitian matrices, and that for all pure rotation point groups, the coefficients can be made real numbers by properly choosing the azimuth angles of symmetry elements of point groups in the coordinate system. We apply the coupling theory of angular momentum to obtain the general formulas of the basis functions of point groups. By use of our formulas, we have calculated the basis functions with half‐integers j from 1/2 to 13/2 of double‐valued irreducible representations for the icosahedral group. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 286–302, 2001

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