"This book presents most of the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics. Both the standard C[superscript [infinite]] pseudodifferential calculus and the analytic microlocal analysis are developed, in a context that 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 Schrodinger operator are also discussed, to further the understanding of new notions or general results by placing 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.

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