Graduate Texts in Mathematics

Quantum Theory for Mathematicians

Authors: Hall, Brian

  • Explains physical ideas in the language of mathematics
  • Provides a self-contained treatment of the necessary mathematics, including spectral theory and Lie theory
  • Contains many exercises that will appeal to graduate students
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eBook $69.99
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  • ISBN 978-1-4614-7116-5
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  • Immediate eBook download after purchase
Hardcover $89.95
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  • ISBN 978-1-4614-7115-8
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  • Usually dispatched within 3 to 5 business days.
Softcover $89.95
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  • ISBN 978-1-4899-9362-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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About this Textbook

Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics.

The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces.  The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.

About the authors

Brian C. Hall is a Professor of Mathematics at the University of Notre Dame.

Reviews

“This book is an introduction to quantum mechanics intended for mathematicians and mathematics students who do not have a particularly strong background in physics. … A well-qualified graduate student can learn a lot from this book. I found it to be clear and well organized, and I personally enjoyed reading it very much.” (David S. Watkins, SIAM Review, Vol. 57 (3), September, 2015)

“This textbook is meant for advanced studies on quantum mechanics for a mathematical readership. The exercises at the end of each chapter make the book especially valuable.” (A. Winterhof, Internationale Mathematischen Nachrichten, Issue 228, 2015)

“There are a few textbooks on quantum theory for mathematicians who are alien to the physical culture … but this modest textbook will surely find its place. All in all, the book is well written and accessible to any interested mathematicians and mathematical graduates.” (Hirokazu Nishimura, zbMATH, Vol. 1273, 2013)


Table of contents (23 chapters)

  • The Experimental Origins of Quantum Mechanics

    Hall, Brian C.

    Pages 1-17

  • A First Approach to Classical Mechanics

    Hall, Brian C.

    Pages 19-52

  • A First Approach to Quantum Mechanics

    Hall, Brian C.

    Pages 53-90

  • The Free Schrödinger Equation

    Hall, Brian C.

    Pages 91-108

  • A Particle in a Square Well

    Hall, Brian C.

    Pages 109-122

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4614-7116-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.95
price for USA
  • ISBN 978-1-4614-7115-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.95
price for USA
  • ISBN 978-1-4899-9362-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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
Quantum Theory for Mathematicians
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
267
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-7116-5
DOI
10.1007/978-1-4614-7116-5
Hardcover ISBN
978-1-4614-7115-8
Softcover ISBN
978-1-4899-9362-5
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XVI, 554
Number of Illustrations and Tables
28 b/w illustrations, 2 illustrations in colour
Topics