## Quantum Theory for Mathematicians

**Author(s):**

Brian C. Hall

**Publisher:**

Springer

**Pages:**554

**Further Actions:**

**Categories:**

### AVAILABLE FORMATS

Paperback - 9781489993625

15 July 2015

* $89.95*

**In stock**

Hardcover - 9781461471158

01 July 2013

* $89.95*

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**In stock**

Ebook - 9781461471165

19 June 2013

* $69.99*

**In stock**

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...

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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.

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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

2 A First Approach to Classical Mechanics

3 A First Approach to Quantum Mechanics

4 The Free Schrödinger Equation

5 A Particle in a Square Well

6 Perspectives on the Spectral Theorem

7 The Spectral Theorem for Bounded Self-Adjoint Operators: Statements

8 The Spectral Theorem for Bounded Sef-Adjoint Operators: Proofs

9 Unbounded Self-Adjoint Operators

10 The Spectral Theorem for Unbounded Self-Adjoint Operators

11 The Harmonic Oscillator

12 The Uncertainty Principle

13 Quantization Schemes for Euclidean Space

14 The Stone–von Neumann Theorem

15 The WKB Approximation

16 Lie Groups, Lie Algebras, and Representations

17 Angular Momentum and Spin

18 Radial Potentials and the Hydrogen Atom

19 Systems and Subsystems, Multiple Particles

V Advanced Topics in Classical and Quantum Mechanics

20 The Path-Integral Formulation of Quantum Mechanics

21 Hamiltonian Mechanics on Manifolds

22 Geometric Quantization on Euclidean Space

23 Geometric Quantization on Manifolds

A Review of Basic Material

References.- Index.

“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)