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  • Book
  • © 1988

Solvable Models in Quantum Mechanics

Authors:

  1. Sergio Albeverio

    1. Faculty of Mathematics and Bielefeld-Bochum Research Center, Ruhr-Universität Bochum, Bochum 1, West Germany

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  2. Friedrich Gesztesy

    1. Institute for Theoretical Physics, University of Graz, Graz, Austria

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  3. Raphael Høegh-Krohn

    1. Institute of Mathematics, University of Oslo, Oslo 3, Norway

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  4. Helge Holden

    1. Institute of Mathematics, University of Trondheim, Trondheim-NTH, Norway

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Part of the book series: Theoretical and Mathematical Physics (TMP)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xiv
    PDF

  2. Introduction

    1. Introduction

      • Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 1-8

  3. The One-Center Point Interaction

    1. Front Matter

      Pages 9-9
      PDF

    2. The One-Center Point Interaction in Three Dimensions

      • Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 11-51

    3. Coulomb Plus One-Center Point Interaction in Three Dimensions

      • Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 52-74

    4. The One-Center δ-Interaction in One Dimension

      • Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 75-90

    5. The One-Center δ’-Interaction in One Dimension

      • Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 91-96

    6. The One-Center Point Interaction in Two Dimensions

      • 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
      PDF

    2. Finitely Many Point Interactions in Three Dimensions

      • Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 109-139

    3. Finitely Many δ-Interactions in One Dimension

      • Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 140-153

    4. Finitely Many δ’-Interactions in One Dimension

      • Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 154-159

    5. Finitely Many Point Interactions in Two Dimensions

      • 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
      PDF

    2. Infinitely Many Point Interactions in Three Dimensions

      • Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 169-252

    3. Infinitely Many δ-Interactions in One Dimension

      • Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 253-306

    4. Infinitely Many δ’-Interactions in One Dimension

      • Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 307-323

    5. Infinitely Many Point Interactions in Two Dimensions

      • Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 324-333

    6. Random Hamiltonians with Point Interactions

      • Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden
      Pages 334-354

  6. Back Matter

    Pages 355-452
    PDF
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About this book

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.
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Keywords

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Authors and Affiliations

  • Faculty of Mathematics and Bielefeld-Bochum Research Center, Ruhr-Universität Bochum, Bochum 1, West Germany

    Sergio Albeverio

  • Institute for Theoretical Physics, University of Graz, Graz, Austria

    Friedrich Gesztesy

  • Institute of Mathematics, University of Oslo, Oslo 3, Norway

    Raphael Høegh-Krohn

  • Institute of Mathematics, University of Trondheim, Trondheim-NTH, Norway

    Helge Holden

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Bibliographic Information

  • Book Title: Solvable Models in Quantum Mechanics

  • Authors: Sergio Albeverio, Friedrich Gesztesy, Raphael Høegh-Krohn, Helge Holden

  • Series Title: Theoretical and Mathematical Physics

  • DOI: https://doi.org/10.1007/978-3-642-88201-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1988

  • Softcover ISBN: 978-3-642-88203-6Published: 04 May 2012

  • eBook ISBN: 978-3-642-88201-2Published: 06 December 2012

  • Series ISSN: 1864-5879

  • Series E-ISSN: 1864-5887

  • Edition Number: 1

  • Number of Pages: XIV, 452

  • Number of Illustrations: 44 b/w illustrations

  • Topics: Quantum Physics, Quantum Information Technology, Spintronics

  • Industry Sectors: Aerospace, Electronics, IT & Software

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Buy it now

eBook USD 89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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