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An Introduction to Semiclassical and Microlocal Analysis (CMS Books in Mathematics)by Andre Martinez
Synopses & ReviewsPublisher Comments:This book presents most of the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics. Both the standard C? pseudodifferential calculus and the analytic microlocal analysis are developed, in a context which remains intentionally global so that only the relevant difficulties of the theory are encountered. The originality lies in the fact that the main features of analytic microlocal analysis are derived from a single and elementary a priori estimate. Various exercises illustrate the chief results of each chapter while introducing the reader to further developments of the theory. Applications to the study of the Schrödinger operator are also discussed, to further the understanding of new notions or general results by replacing them in the context of quantum mechanics. This book is aimed at nonspecialists of the subject and the only required prerequisite is a basic knowledge of the theory of distributions. André Martinez is currently Professor of Mathematics at the University of Bologna, Italy, after having moved from France where he was Professor at ParisNord University. He has published many research articles in semiclassical quantum mechanics, in particular related to the BornOppenheimer approximation, phasespace tunneling, scattering theory and resonances.
Synopsis:This book presents most of the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics. Both the standard C8 pseudodifferential calculus and the analytic microlocal analysis is developed, in a context which remains intentionally global so that only the relevant difficulties of the theory are encountered. The originality lies in the fact that the main features of analytic microlocal analysis are derived from a single and elementary a priori estimate. Various exercises illustrate the chief results of each chapter while introducing the reader to further developments of the theory. This book is aimed at nonspecialists of the subject and the only required prerequisite is a basic knowledge of the theory of distributions.
Synopsis:This book presents the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics in a pedagogical, way and is mainly addressed to nonspecialists in the subject. It is based on lectures taught by the author over several years, and includes many exercises providing outlines of useful applications of the semiclassical theory.
Table of ContentsIntroduction * Semiclassical Pseudodifferential Calculus * Microlocalization * Applications to the Solutions of Analytic Linear PDEs * Complements: Symplectic Aspects * Appendix: List of Formulae * Bibliography * Index * List of Notations
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