Autour de l'approximation semi-classique / Didier Robert

Auteur: Robert, Didier (1964-) - AuteurType de document: MonographieCollection: Progress in mathematics ; 68Langue: françaisPays: Etats UnisÉditeur: Boston : Birkhauser, 1987Description: 1 vol. (IX-328 p.) ; 24 cm ISBN: 0817633545 ; rel. Note: This book is devoted to mathematical investigation of the quasi-classical limit of quantum mechanics. In Chapter I a short introduction into the principles of non-relativistic quantum theory is presented. In Chapter II "h-admissible operators" calculus of scalar admissible h-pseudo- differential operators and of Fourier integral operators are developed. In Chapter III "Functional calculus for h-admissible operators" a class of selfadjoint admissible h-pseudo-differential operators is introduced and it is proved that admissible functions of operators of this class are admissible h-pseudo-differential operators too; in particular resolvents and complex powers of operators are considered. Appendix 1 "Essentially selfadjoint operators" and Appendix 2 "Essential spectrum" contain certain classical functional-analytic results. (Zentralblatt)Bibliographie: Bibliography: p. [317]-328. Sujets MSC: 81Q10 Quantum theory -- General mathematical topics and methods in quantum theory -- Selfadjoint operator theory in quantum theory, including spectral analysis
35P20 Partial differential equations -- Spectral theory and eigenvalue problems -- Asymptotic distribution of eigenvalues and eigenfunctions
35J10 Partial differential equations -- Elliptic equations and systems -- Schrödinger operator
58J37 Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Perturbations; asymptotics
58J40 Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Pseudodifferential and Fourier integral operators on manifolds
81Q15 Quantum theory -- General mathematical topics and methods in quantum theory -- Perturbation theories for operators and differential equations
En-ligne: sur Numir | Zentralblatt | MathSciNet
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This book is devoted to mathematical investigation of the quasi-classical limit of quantum mechanics. In Chapter I a short introduction into the principles of non-relativistic quantum theory is presented. In Chapter II "h-admissible operators" calculus of scalar admissible h-pseudo- differential operators and of Fourier integral operators are developed. In Chapter III "Functional calculus for h-admissible operators" a class of selfadjoint admissible h-pseudo-differential operators is introduced and it is proved that admissible functions of operators of this class are admissible h-pseudo-differential operators too; in particular resolvents and complex powers of operators are considered. Appendix 1 "Essentially selfadjoint operators" and Appendix 2 "Essential spectrum" contain certain classical functional-analytic results. (Zentralblatt)

Bibliography: p. [317]-328

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