Solvable Models in Quantum Mechanics

  • Sergio Albeverio
  • Friedrich Gesztesy
  • Raphael Høegh-Krohn
  • Helge Holden

Part of the Texts and Monographs in Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Introduction

    1. Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 1-8
  3. The One-Center Point Interaction

    1. Front Matter
      Pages 9-9
    2. Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 11-51
    3. Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 52-74
    4. Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 75-90
    5. Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 91-96
    6. Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 97-105
  4. Point Interactions with a Finite Number of Centers

    1. Front Matter
      Pages 107-107
    2. Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 109-139
    3. Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 140-153
    4. Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 154-159
    5. Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 160-166
  5. Point Interactions with Infinitely Many Centers

    1. Front Matter
      Pages 167-167
    2. Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 169-252
    3. Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 253-306
    4. Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 307-323
    5. Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 324-333
    6. Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 334-354
  6. Back Matter
    Pages 355-452

About this book

Introduction

Next to the harmonic oscillator and the Coulomb potential the class of two-body models with point interactions is the only one where complete solutions are available. All mathematical and physical quantities can be calculated explicitly which makes this field of research important also for more complicated and realistic models in quantum mechanics. The detailed results allow their implementation in numerical codes to analyse properties of alloys, impurities, crystals and other features in solid state quantum physics. This monograph presents in a systematic way the mathematical approach and unifies results obtained in recent years. The student with a sound background in mathematics will get a deeper understanding of Schrödinger Operators and will see many examples which may eventually be used with profit in courses on quantum mechanics and solid state physics. The book has textbook potential in mathematical physics and is suitable for additional reading in various fields of theoretical quantum physics.

Keywords

Potential crystal mathematical physics mechanics quantum mechanics quantum physics scattering scattering theory

Authors and affiliations

  • Sergio Albeverio
    • 1
  • Friedrich Gesztesy
    • 2
  • Raphael Høegh-Krohn
    • 3
  • Helge Holden
    • 4
  1. 1.Faculty of Mathematics and Bielefeld-Bochum Research CenterRuhr-Universität BochumBochum 1West Germany
  2. 2.Institute for Theoretical PhysicsUniversity of GrazGrazAustria
  3. 3.Institute of MathematicsUniversity of OsloOslo 3Norway
  4. 4.Institute of MathematicsUniversity of TrondheimTrondheim-NTHNorway

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-88201-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-88203-6
  • Online ISBN 978-3-642-88201-2
  • Series Print ISSN 1864-5879
  • Series Online ISSN 1864-5887
  • About this book