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Canonical generator states and their symmetry adaptation
Author(s) -
Matsen F. A.
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.560260808
Subject(s) - irreducible representation , unitary state , unitary transformation , basis (linear algebra) , generator (circuit theory) , symmetry (geometry) , representation (politics) , homogeneous space , pure mathematics , unitary representation , operator (biology) , matrix (chemical analysis) , algebra over a field , symmetry group , representation theory , mathematics , reflection (computer programming) , group (periodic table) , group theory , physics , lie group , quantum mechanics , computer science , chemistry , geometry , repressor , law , quantum , power (physics) , biochemistry , chromatography , political science , transcription factor , programming language , politics , gene
Canonical generator states provide an overcomplete, nonorthonormal basis for the irreducible representation spaces of the unitary group. The matrix representation of any unitary‐group operator in the generator basis can be directly computed by Lie algebra techniques and can be converted, if desired, to a representation over Gel'fand states by inverting the Moshinsky–Nagel transformation. Application is made to the symmetry adaptation of the Hubbard allyl radical with respect to reflection, guasispin, and R (3) symmetries.