Unitary group approach to general system partitioning. I. Calculation of  U ( n  =  n  1  +  n  2 ):  U ( n  1 ) ×  u ( n  2 ) reduced matrix elements and reduced wigner coefficients | Zendy

Gould M. D. | Zendy; Paldus J. | Zendy

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Unitary group approach to general system partitioning. I. Calculation of U ( n = n 1 + n 2 ): U ( n 1 ) × u ( n 2 ) reduced matrix elements and reduced wigner coefficients

Author(s) -

Gould M. D.,

Paldus J.

Publication year - 1986

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.560300304

Subject(s) - unitary group , group (periodic table) , mathematics , unitary state , unitary matrix , symmetry (geometry) , matrix (chemical analysis) , symmetry group , mathematical physics , combinatorics , series (stratigraphy) , quantum mechanics , function (biology) , physics , pure mathematics , chemistry , geometry , paleontology , chromatography , evolutionary biology , political science , law , biology

This paper is the first in a series of two directed toward a unitary calculus for group‐function‐type approaches to the many‐electron correlation problem. In this paper we present a complete derivation of the matrix elements of the U ( n = n 1 + n 2 ) generators, for the representations approapriate to many‐electron systems, in a basis symmetry adapted to the subgroup U ( n 1 ) × U ( n 2 ). Explicit formulae for the fundamental U ( n ): U ( n 1 ) × U ( n 2 ) reduced Wigner coefficients, which are needed for the general multishell problem, are also obtained. The symmetry properties of the reduced Wigner coefficients and reduced matrix elements are investigated, and a suitable phase convention is given.

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