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-xiii
  2. Stephen J. Gustafson, Israel Michael Sigal
    Pages 1-7
  3. Stephen J. Gustafson, Israel Michael Sigal
    Pages 9-17
  4. Stephen J. Gustafson, Israel Michael Sigal
    Pages 19-25
  5. Stephen J. Gustafson, Israel Michael Sigal
    Pages 27-40
  6. Stephen J. Gustafson, Israel Michael Sigal
    Pages 41-45
  7. Stephen J. Gustafson, Israel Michael Sigal
    Pages 47-59
  8. Stephen J. Gustafson, Israel Michael Sigal
    Pages 61-73
  9. Stephen J. Gustafson, Israel Michael Sigal
    Pages 75-87
  10. Stephen J. Gustafson, Israel Michael Sigal
    Pages 89-98
  11. Stephen J. Gustafson, Israel Michael Sigal
    Pages 99-105
  12. Stephen J. Gustafson, Israel Michael Sigal
    Pages 107-125
  13. Stephen J. Gustafson, Israel Michael Sigal
    Pages 127-140
  14. Stephen J. Gustafson, Israel Michael Sigal
    Pages 141-148
  15. Stephen J. Gustafson, Israel Michael Sigal
    Pages 149-154
  16. Stephen J. Gustafson, Israel Michael Sigal
    Pages 155-171
  17. Stephen J. Gustafson, Israel Michael Sigal
    Pages 173-189
  18. Stephen J. Gustafson, Israel Michael Sigal
    Pages 191-208
  19. Stephen J. Gustafson, Israel Michael Sigal
    Pages 209-226
  20. Stephen J. Gustafson, Israel Michael Sigal
    Pages 227-245

About this book

Introduction

The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline.

Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content.

It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include many-body systems, modern perturbation theory, path integrals, the theory of resonances, quantum statistics, mean-field theory, second quantization, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group.

With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. The last four chapters could also serve as an introductory course in quantum field theory.

Keywords

Schrödinger equation quantization quantum mechanics spectral theory

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-21866-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-21865-1
  • Online ISBN 978-3-642-21866-8
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book