An Introduction to Semiclassical and Microlocal Analysis

  • André Martinez

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-viii
  2. André Martinez
    Pages 1-8
  3. André Martinez
    Pages 9-67
  4. André Martinez
    Pages 69-103
  5. André Martinez
    Pages 141-167
  6. André Martinez
    Pages 169-173
  7. Back Matter
    Pages 175-191

About this book

Introduction

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.

Keywords

Boundary value problem Microlocal analysis calculus differential equation distribution quantum physics

Authors and affiliations

  • André Martinez
    • 1
  1. 1.Department of MathematicsUniversity of BolognaBolognaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-4495-8
  • Copyright Information Springer-Verlag New York 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2961-7
  • Online ISBN 978-1-4757-4495-8
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book