Universitext

An Introduction to Semiclassical and Microlocal Analysis

Authors: Bach, André

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About this Textbook

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.

Reviews

From the reviews:

"The book is very clearly written, and is indeed much simpler than most of others. … this is an excellent book, suitable even for students with a poor background in the subject. In my opinion, every department offering courses on partial differential equations or asymptotic analysis should have it in the library. It will be very useful to all mathematicians working in semi-classical or microlocal analysis … ." (Yuri Safarov, Bulletin of the London Mathematical Society, Issue 35, 2003)

"This is a concise and accessible book on the basic techniques of semiclassical and microlocal analysis. … An appendix provides a useful summary of the major formulas used in the text. Each chapter is followed by a collection of provocative and well chosen exercises. The exercises are essential for understanding the work and provide important applications. … the text does provide a very readable, clear, and concise introduction to semiclassical and microlocal analysis." (Peter D. Hislop, Mathematical Reviews, 2003 b)

"The contents of the book correspond to a course at Ph. D. Level, given by the author at the Universities of Bologna and Paris-Nord. … the book collects in an original way standard results and new aspects of semi-classical microlocal analysis; the reading is suggested to non-specialists as well." (L. Rodino, Zentralblatt MATH, Vol. 994 (19), 2002)

"This book presents most of the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics. … 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 … ." (L’ Enseignement Mathematique, Vol. 48 (1-2), 2002)

"The book under review consists of lecture notes corresponding to a course taught for several years at the universities of Paris-Nord (France) and Bologna (Italy). It is addressed mainly to non-specialists in the subject, and the prerequisites are essentially reduced to the basic notions of the theory of distributions. … The author tries to make clear how the things work and show examples where they can be applied. It is nicely written … . the book can be highly recommended." (J. Synnatzschke, Zeitschrift für Analysis und ihre Anwendungen – ZAA, Vol. 21 (3), 2002)


Table of contents (6 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4757-4495-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-0-387-95344-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA
  • ISBN 978-1-4419-2961-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Semiclassical and Microlocal Analysis
Authors
Series Title
Universitext
Copyright
2002
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-4495-8
DOI
10.1007/978-1-4757-4495-8
Hardcover ISBN
978-0-387-95344-1
Softcover ISBN
978-1-4419-2961-7
Series ISSN
0172-5939
Edition Number
1
Number of Pages
VIII, 191
Topics