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Usage de l'Algèbre de Lie su ( n ) dans l'Etude des Systèmes Quantiques à n Etats. II. Transformation de l'Espace des Observables, Problèmes d'Evolution
Author(s) -
Tillieu Jacques,
Van Groenendael Augugstin
Publication year - 1983
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.560230511
Subject(s) - lie algebra , mathematics , pure mathematics , unitary state , transformation (genetics) , quantum , hilbert space , algebra over a field , unitary transformation , space (punctuation) , observable , relation (database) , mathematical physics , physics , quantum mechanics , computer science , biochemistry , chemistry , political science , law , gene , database , operating system
In the previous paper we examined, for a quantum system, the relation between its n ‐dimensional state space and the su ( n ) Lie algebra. The present paper is devoted to relations between unitary transformations in the state space and orthogonal transformations in Lie's algebra. Two cases can happen. First, the transformations are independently chosen in the two spaces; this amounts to changing the former relation. On the other hand, the relation is maintained and the unitary operators are then related to some of the orthogonal operators. This second case is used to study the evolution operators.