Autour de l'approximation semi-classique / Didier Robert

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