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An Introduction to Semiclassical and Microlocal Analysis

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An Introduction to Semiclassical and Microlocal Analysis

An Introduction to Semiclassical and Microlocal Analysis

André Martinez

190 pages, parution le 21/01/2002

Résumé

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.

Contents

  • Introduction.
  • Semiclassical Pseudodifferential Calculus.
  • Microlocalization.
  • Applications to the Solutions of Analytic Linear PDEs.
  • Complements: Symplectic Aspects.
  • Appendix: List of Formulae.
  • Bibliography.
  • Index.
  • List of Notations.

L'auteur - André Martinez

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.

Caractéristiques techniques

  PAPIER
Éditeur(s) Springer
Auteur(s) André Martinez
Parution 21/01/2002
Nb. de pages 190
Format 16 x 24
Couverture Relié
Poids 400g
Intérieur Noir et Blanc
EAN13 9780387953441
ISBN13 978-0-387-95344-1

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