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Mathematical Concepts of Quantum Mechanics

  • Stephen J. Gustafson
  • Israel Michael Sigal

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-X
  2. Stephen J. Gustafson, Israel Michael Sigal
    Pages 1-11
  3. Stephen J. Gustafson, Israel Michael Sigal
    Pages 13-24
  4. Stephen J. Gustafson, Israel Michael Sigal
    Pages 25-29
  5. Stephen J. Gustafson, Israel Michael Sigal
    Pages 31-33
  6. Stephen J. Gustafson, Israel Michael Sigal
    Pages 35-59
  7. Stephen J. Gustafson, Israel Michael Sigal
    Pages 61-66
  8. Stephen J. Gustafson, Israel Michael Sigal
    Pages 67-78
  9. Stephen J. Gustafson, Israel Michael Sigal
    Pages 79-94
  10. Stephen J. Gustafson, Israel Michael Sigal
    Pages 95-114
  11. Stephen J. Gustafson, Israel Michael Sigal
    Pages 115-120
  12. Stephen J. Gustafson, Israel Michael Sigal
    Pages 121-134
  13. Stephen J. Gustafson, Israel Michael Sigal
    Pages 135-151
  14. Stephen J. Gustafson, Israel Michael Sigal
    Pages 153-166
  15. Stephen J. Gustafson, Israel Michael Sigal
    Pages 167-196
  16. Stephen J. Gustafson, Israel Michael Sigal
    Pages 197-206
  17. Stephen J. Gustafson, Israel Michael Sigal
    Pages 207-234
  18. Stephen J. Gustafson, Israel Michael Sigal
    Pages 235-238
  19. Back Matter
    Pages 239-249

About this book

Introduction

The first fifteen chapters of these lectures (omitting four to six chapters each year) cover a one term course taken by a mixed group of senior undergraduate and junior graduate students specializing either in mathematics or physics. Typically, the mathematics students have some background in advanced anal­ ysis, while the physics students have had introductory quantum mechanics. To satisfy such a disparate audience, we decided to select material which is interesting from the viewpoint of modern theoretical physics, and which illustrates an interplay of ideas from various fields of mathematics such as operator theory, probability, differential equations, and differential geometry. Given our time constraint, we have often pursued mathematical content at the expense of rigor. However, wherever we have sacrificed the latter, we have tried to explain whether the result is an established fact, or, mathematically speaking, a conjecture, and in the former case, how a given argument can be made rigorous. The present book retains these features.

Keywords

Hilbert space Operator theory Potential Renormalization group Schrödinger equation quantization quantum mechanics spectral theory

Authors and affiliations

  • Stephen J. Gustafson
    • 1
  • Israel Michael Sigal
    • 2
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-55729-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-44160-1
  • Online ISBN 978-3-642-55729-3
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site