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Unitary transformations with the unitary operators depending on projection operators
Author(s) -
Stepanov N. F.
Publication year - 1981
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.560190510
Subject(s) - unitary state , operator (biology) , resolvent , mathematics , hermitian matrix , projection (relational algebra) , unitary operator , operator theory , algebra over a field , simple (philosophy) , pure mathematics , unitarity , unitary transformation , hilbert space , algorithm , physics , quantum mechanics , quantum , chemistry , biochemistry , philosophy , epistemology , repressor , political science , transcription factor , law , gene
Unitary transformations of operators and variables are considered for those cases when a Hermitian operator in the expression U = exp ( i S ) explicitly depends on the projection operators. Some simple examples of such transformations are given and the equations obtained which define projectors (among special sets of them), thus bringing forth better estimations for upper and lower bounds. The unitary transformations are also applied to the reduced resolvent operator and equations are presented for the operators U that minimize the energy functional.