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Unitary group approach to the many‐electron problem. III. Matrix elements of spin‐dependent Hamiltonians
Author(s) -
Gould M. D.,
Chandler G. S.
Publication year - 1984
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.560250613
Subject(s) - basis (linear algebra) , unitary state , matrix (chemical analysis) , spin (aerodynamics) , unitary group , group (periodic table) , physics , electron , quantum mechanics , symmetry (geometry) , spin–orbit interaction , unitary matrix , mathematics , mathematical physics , theoretical physics , chemistry , geometry , law , thermodynamics , chromatography , political science
This is the final paper in a series of three directed toward the evaluation of spin‐dependent Hamiltonians. In this paper we derive the reduced matrix elements of the U (2 n ) generators in a basis symmetry adapted to the subgroup U ( n ) × U (2) (i.e., spin‐orbit basis), for the representations appropriate to many‐electron systems. This enables a direct evaluation of the matrix elements of spin‐dependent Hamiltonians in the spin‐orbit basis. An alternative (indirect) method, which employs the use of U (2 n ) ↓ U ( n ) × U (2) subduction coefficients, is also discussed.