Authors:
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
Part of the book series: Graduate Texts in Mathematics (GTM, volume 267)
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Table of contents (23 chapters)

Front Matter
About this book
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.
Keywords
 Hilbert space
 Lie groups
 Stonevon Neumann theorem
 WKB approximation
 geometric quantization
 quantum mechanics
 spectral theorem
 unbounded operators
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)
Authors and Affiliations

Department of Mathematics, University of Notre Dame, Notre Dame, USA
Brian C. Hall
About the author
Bibliographic Information
Book Title: Quantum Theory for Mathematicians
Authors: Brian C. Hall
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/9781461471165
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2013
Hardcover ISBN: 9781461471158Published: 19 June 2013
Softcover ISBN: 9781489993625Published: 15 July 2015
eBook ISBN: 9781461471165Published: 19 June 2013
Series ISSN: 00725285
Series EISSN: 21975612
Edition Number: 1
Number of Pages: XVI, 554
Number of Illustrations: 28 b/w illustrations, 2 illustrations in colour
Topics: Mathematical Physics, Quantum Physics, Functional Analysis, Topological Groups and Lie Groups, Mathematical Methods in Physics