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Schrödinger Operators

With Applications to Quantum Mechanics and Global Geometry

  • Hans L. Cycon
  • Richard G. Froese
  • Werner Kirsch
  • Barry Simon
  • Hans L. Cycon

Part of the Theoretical,Mathematical Physics book series (TMP)

About this book

Introduction

A complete understanding of Schrödinger operators is a necessary prerequisite for unveiling the physics of nonrelativistic quanturn mechanics. Furthermore recent research shows that it also helps to deepen our insight into global differential geometry. This monograph written for both graduate students and researchers summarizes and synthesizes the theory of Schrödinger operators emphasizing the progress made in the last decade by Lieb, Enss, Witten and others. Besides general properties, the book covers, in particular, multiparticle quantum mechanics including bound states of Coulomb systems and scattering theory, quantum mechanics in constant electric and magnetic fields, Schrödinger operators with random and almost periodic potentials and, finally, Schrödinger operator methods in differential geometry to prove the Morse inequalities and the index theorem.

Keywords

Potential differential geometry geometry magnetic field mechanics quantum mechanics scattering scattering theory

Authors and affiliations

  • Hans L. Cycon
    • 1
    • 2
    • 3
  • Richard G. Froese
    • 4
  • Werner Kirsch
  • Barry Simon
    • 5
  • Hans L. Cycon
    • 1
    • 2
    • 3
  1. 1.Technische Universität BerlinHans L.CyconBerlin 12Germany
  2. 2.University of Bochum; Institute of MathematicsProf.Dr. Werner KirschBochumGermany
  3. 3.California Institute of Technology; Department of MathematicsProf. Dr. Barry SimonPasadenaUSA
  4. 4.University of British Columbia, Department of MathematicsDr. Richard G.FroeseVancouver, B.C.USA
  5. 5.California Institute of TechnologyCalifornia Institute of TechnologyPasadenaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-77522-5
  • Copyright Information Springer-Verlag 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-16758-7
  • Online ISBN 978-3-540-77522-5
  • Series Print ISSN 0172-5998
  • Buy this book on publisher's site
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