Universitext

Mathematical Concepts of Quantum Mechanics

Authors: Gustafson, Stephen J., Sigal, Israel Michael

  • A very readable introduction to modern mathematical topics in quantum mechanics
  • Solves the problem of how to teach quantum mechanics to mathematically oriented students in an optimal way
  • Shows how the mathematical treatment of quantum mechanics brings insights to physics
  • Useful guide to the literature
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Buy this book

eBook n/a
  • ISBN 978-3-642-21866-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
Softcover n/a
  • ISBN 978-3-642-21865-1
  • Free shipping for individuals worldwide
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

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.

Reviews

From the reviews of the second edition:

“This is the second edition of a readable introduction to modern mathematical topics in quantum mechanics intended for students of mathematics or physics. In comparison to the first edition the authors have tried to make the book more self-contained by adding further proofs and background material. … The overall style has not changed and with the extra background material it is now even better suited as the basis of a graduate course.” (G. Teschl, Monatshefte für Mathematik, Vol. 166 (2), May, 2012)

Table of contents (25 chapters)

  • Physical Background

    Gustafson, Stephen J. (et al.)

    Pages 1-7

  • Dynamics

    Gustafson, Stephen J. (et al.)

    Pages 9-17

  • Observables

    Gustafson, Stephen J. (et al.)

    Pages 19-25

  • Quantization

    Gustafson, Stephen J. (et al.)

    Pages 27-40

  • Uncertainty Principle and Stability of Atoms and Molecules

    Gustafson, Stephen J. (et al.)

    Pages 41-45

Buy this book

eBook n/a
  • ISBN 978-3-642-21866-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
Softcover n/a
  • ISBN 978-3-642-21865-1
  • Free shipping for individuals worldwide
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Concepts of Quantum Mechanics
Authors
Series Title
Universitext
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-21866-8
DOI
10.1007/978-3-642-21866-8
Softcover ISBN
978-3-642-21865-1
Series ISSN
0172-5939
Edition Number
2
Number of Pages
XIII, 382
Number of Illustrations and Tables
37 b/w illustrations
Topics