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Schrödinger Operators

With Application to Quantum Mechanics and Global Geometry

  • Textbook
  • © 1987

Overview

Authors:
  1. Hans L. Cycon

    1. Technische Universität Berlin, Hans L.Cycon, Berlin 12, Germany
      University of Bochum; Institute of Mathematics, Prof.Dr. Werner Kirsch, Bochum, Germany
      California Institute of Technology; Department of Mathematics, Prof. Dr. Barry Simon, Pasadena, USA

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  2. Richard G. Froese

    1. University of British Columbia, Department of Mathematics, Dr. Richard G.Froese, Vancouver, B.C., USA

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  3. Werner Kirsch
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  4. Barry Simon

    1. California Institute of Technology, California Institute of Technology, Pasadena, USA

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  5. Hans L. Cycon

    1. Technische Universität Berlin, Hans L.Cycon, Berlin 12, Germany
      University of Bochum; Institute of Mathematics, Prof.Dr. Werner Kirsch, Bochum, Germany
      California Institute of Technology; Department of Mathematics, Prof. Dr. Barry Simon, Pasadena, USA

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    You can also search for this author in PubMed   Google Scholar

  • 2nd updated edition of a classic book.
  • Written by the leading researchers in the field.

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

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-XI
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  2. Self-Adjointness

    Pages 1-12

  3. Lp-Properties of Eigenfunctions, and All That

    Pages 13-26

  4. Geometric Methods for Bound States

    Pages 27-59

  5. Local Commutator Estimates

    Pages 60-88

  6. Phase Space Analysis of Scattering

    Pages 89-114

  7. Magnetic Fields

    Pages 115-134

  8. Electric Fields

    Pages 135-152

  9. Complex Scaling

    Pages 153-167

  10. Random Jacobi Matrices

    Pages 168-202

  11. Almost Periodic Jacobi Matrices

    Pages 203-223

  12. Witten’s Proof of the Morse Inequalities

    Pages 224-244

  13. Patodi’s Proof of the Gauss-Bonnet-Chern Theorem and Superproofs of Index Theorems

    Pages 245-306

  14. Back Matter

    Pages 307-329
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Keywords

About this book

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.

Authors and Affiliations

  • Technische Universität Berlin, Hans L.Cycon, Berlin 12, Germany

    Hans L. Cycon, Hans L. Cycon

  • University of Bochum; Institute of Mathematics, Prof.Dr. Werner Kirsch, Bochum, Germany

    Hans L. Cycon, Hans L. Cycon

  • California Institute of Technology; Department of Mathematics, Prof. Dr. Barry Simon, Pasadena, USA

    Hans L. Cycon, Hans L. Cycon

  • University of British Columbia, Department of Mathematics, Dr. Richard G.Froese, Vancouver, B.C., USA

    Richard G. Froese

  • California Institute of Technology, California Institute of Technology, Pasadena, USA

    Barry Simon

Bibliographic Information

  • Book Title: Schrödinger Operators

  • Book Subtitle: With Application to Quantum Mechanics and Global Geometry

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

  • Series Title: Theoretical and Mathematical Physics

  • DOI: https://doi.org/10.1007/978-3-540-77522-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • eBook ISBN: 978-3-540-77522-5Published: 19 August 2009

  • Series ISSN: 1864-5879

  • Series E-ISSN: 1864-5887

  • Edition Number: 1

  • Number of Pages: IX

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Quantum Physics, Quantum Information Technology, Spintronics

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