 Explains physical ideas in the language of mathematics
 Provides a selfcontained 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

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 selfadjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the pathintegral 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 wellqualified 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
Pages 117

A First Approach to Classical Mechanics
Pages 1952

A First Approach to Quantum Mechanics
Pages 5390

The Free Schrödinger Equation
Pages 91108

A Particle in a Square Well
Pages 109122

Table of contents (23 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Quantum Theory for Mathematicians
 Authors

 Brian C. Hall
 Series Title
 Graduate Texts in Mathematics
 Series Volume
 267
 Copyright
 2013
 Publisher
 SpringerVerlag New York
 Copyright Holder
 Springer Science+Business Media New York
 eBook ISBN
 9781461471165
 DOI
 10.1007/9781461471165
 Hardcover ISBN
 9781461471158
 Softcover ISBN
 9781489993625
 Series ISSN
 00725285
 Edition Number
 1
 Number of Pages
 XVI, 554
 Number of Illustrations
 28 b/w illustrations, 2 illustrations in colour
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