C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians

  • Werner O. Amrein
  • Anne Boutet de Monvel
  • Vladimir Georgescu

Part of the Progress in Mathematics book series (PM, volume 135)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
    Pages 1-28
  3. Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
    Pages 29-72
  4. Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
    Pages 73-170
  5. Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
    Pages 171-190
  6. Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
    Pages 191-233
  7. Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
    Pages 235-265
  8. Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
    Pages 267-356
  9. Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
    Pages 357-399
  10. Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
    Pages 401-432
  11. Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
    Pages 433-443
  12. Back Matter
    Pages 445-464

About this book

Introduction

The relevance of commutator methods in spectral and scattering theory has been known for a long time, and numerous interesting results have been ob­ tained by such methods. The reader may find a description and references in the books by Putnam [Pu], Reed-Simon [RS] and Baumgartel-Wollenberg [BW] for example. A new point of view emerged around 1979 with the work of E. Mourre in which the method of locally conjugate operators was introduced. His idea proved to be remarkably fruitful in establishing detailed spectral properties of N-body Hamiltonians. A problem that was considered extremely difficult be­ fore that time, the proof of the absence of a singularly continuous spectrum for such operators, was then solved in a rather straightforward manner (by E. Mourre himself for N = 3 and by P. Perry, 1. Sigal and B. Simon for general N). The Mourre estimate, which is the main input of the method, also has consequences concerning the behaviour of N-body systems at large times. A deeper study of such propagation properties allowed 1. Sigal and A. Soffer in 1985 to prove existence and completeness of wave operators for N-body systems with short range interactions without implicit conditions on the potentials (for N = 3, similar results were obtained before by means of purely time-dependent methods by V. Enss and by K. Sinha, M. Krishna and P. Muthuramalingam). Our interest in commutator methods was raised by the major achievements mentioned above.

Keywords

PDE algebra calculus functional analysis quantum mechanics

Authors and affiliations

  • Werner O. Amrein
    • 1
  • Anne Boutet de Monvel
    • 2
  • Vladimir Georgescu
    • 2
  1. 1.Ecole de PhysiqueUniversité de GenèveGenève 4Switzerland
  2. 2.Institut de Mathématiques de Paris-Jussieu, C.N.R.S. UMR 9994Université Paris VII Denis DiderotParis Cedex 05France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-7762-6
  • Copyright Information Birkhäuser Basel 1996
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-0348-7764-0
  • Online ISBN 978-3-0348-7762-6
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • About this book