An Introduction to Semiclassical and Microlocal Analysis

Semi-classical analysis has become a mathematical tool for dealing with a variety of asymptotic problems. This book provides a systematic and extremely useful presentation of the theory in its traditional setting motivated by quantum mechanics. Both the standard C8 pseudodifferential calculus and the analytic microlocal analysis are developed, while the author replaces the delicate local theory with a more straightforward global theory. The only prerequisite required is a basic knowledge of the theory of distributions.

Addressed to non-specialists detailed exercises at the end of the main chapters proofs presented have been made as simple as possible introduces tools useful in the study of phase space tunneling Includes supplementary material: sn.pub/extras

Klappentext
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 non-specialists 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 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.

Inhalt
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.