- 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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- About this Textbook
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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
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Brian C. Hall is a Professor of Mathematics at the University of Notre Dame.
- Reviews
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“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)
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The Experimental Origins of Quantum Mechanics
Pages 1-17
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A First Approach to Classical Mechanics
Pages 19-52
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A First Approach to Quantum Mechanics
Pages 53-90
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The Free Schrödinger Equation
Pages 91-108
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A Particle in a Square Well
Pages 109-122
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Table of contents (23 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Quantum Theory for Mathematicians
- Authors
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- Brian C. Hall
- Series Title
- Graduate Texts in Mathematics
- Series Volume
- 267
- Copyright
- 2013
- Publisher
- Springer-Verlag New York
- Copyright Holder
- Springer Science+Business Media, LLC, part of Springer Nature
- 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
- 28 b/w illustrations, 2 illustrations in colour
- Topics
