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  • 1
    Electronic Resource
    Electronic Resource
    Usage de l'Algègbre de Lie su (n) Dans l'Etude des Systèmes Quantiques à n Etats. I. Quelques Conséquences Générales (1983)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. 1807-1816 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In an n level quantum system there is a relation between each density operator and an element of su (n) Lie algebra. This relation is also established between Cartan's subalgebras and the complete sets of compatible observables. A scalar product is then defined in this algebra in order to introduce orthonormal bases and to simplify many calculations about expectation values of observables. Therefore simple general rules were established which show how to determine (completely or partly), from linearly independent observables, the density operator of the system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560230510
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    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 (1983)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. 1817-1827 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560230511
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Usage de l'Algèbre de Lie su (n) dans l'Etude des Systèmes Quantiques à n Etats. V. Application aux Systèmes composés (1985)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 28 (1985), S. 269-286 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: We adapt the use of the Lie algebra su (n) we proposed in former papers to a system made up of two subsystems (respectively, nA and nB states). We show how reduced density operators, correlation problems, and overall and reduced evolution equations, may be made precise with this formalism.
    Notes: L'usage de l'algèbre de Lie su (n), proposé dans les articles précédents, est adapté a l'étude d'un système formé de deux sous-systèmes, respectivement à nA et nB états. On montre comment diverses notions (opérateurs-densités réduits, problèmes de corrélation, équations d'évolution globales et réduites) peuvent être précisées grâce au formalisme introduit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560280209
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  • 4
    Electronic Resource
    Electronic Resource
    Usage de l'algkbre de lie su(n) dans l'etude des systèmes quantiques à n etats. III. Définition et obtention des constantes du mouvement conjoncturelles (1984)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 26 (1984), S. 479-488 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: From the density operator, some constants of the motion are defined and established. We suggest calling them conjunctural constants of the motion. It is proved that no more than n - 1 of them can be linearly independent. Using su(m) (m 〈 n ) subalgebra associated with the Hamiltonian-operator, it is shown how conjunctural constants of the motion can be expressed in terms of the coherence vector components.
    Notes: A partir de I'opérateur-densité d'un système quantique à n états, sont définies et calcultes des constantes du mouvement pour lesquelles est proposée I'appellation nouvelle de conjoncturelles. On établit qu'il en existe au maximum n - 1 linéairement indépendantes. A I'aide des sous-algèbres su(m) (m 〈 n ), on montre comment il est possible d'introduire, suivant la forme de I'hamiltonien, des constantes du mouvement conjoncturelles reliées aux composantes du vecteur de cohérence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560260406
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  • 5
    Electronic Resource
    Electronic Resource
    Usage de l'algèbre de lie SU(n) dans l'etude des systèmes quantiques a n etats. VII: Sur le “problème inverse” (1989)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 35 (1989), S. 331-337 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Through a formalism developed in formr papers, some problems, set by the determination, from experimental data of the evolution equation of an n-states quantum system are considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560350210
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    Paper (German National Licenses)
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