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 Schrรถdinger 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 non-specialists of the subject and the only required prerequisite is a basic knowledge of the theory of distributions. Andrรฉ Martinez is currently Professor of Mathematics at the University of Bologna, Italy, after having moved from France where he was Professor at Paris-Nord University. He has published many research articles in semiclassical quantum mechanics, in particular related to the Born-Oppenheimer approximation, phase-space tunneling, scattering theory and resonances
CONTENT
1 Introduction -- 2 Semiclassical Pseudodifferential Calculus -- 3 Microlocalization -- 4 Applications to the Solutions of Analytic Linear PDEs -- 5 Complements: Symplectic Aspects -- 6 Appendix: List of Formulae -- List of Notation
SUBJECT
Mathematics
Mathematical analysis
Analysis (Mathematics)
Manifolds (Mathematics)
Complex manifolds
Quantum physics
Mathematics
Analysis
Manifolds and Cell Complexes (incl. Diff.Topology)
