**Graduate Studies in Mathematics**

Volume: 157;
2014;
356 pp;
Hardcover

MSC: Primary 81; 46; 34; 47;

Print ISBN: 978-1-4704-1704-8

Product Code: GSM/157

List Price: $67.00

Individual Member Price: $53.60

**Electronic ISBN: 978-1-4704-1888-5
Product Code: GSM/157.E**

List Price: $67.00

Individual Member Price: $53.60

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#### Supplemental Materials

# Mathematical Methods in Quantum Mechanics: With Applications to Schrödinger Operators, Second Edition

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*Gerald Teschl*

Quantum mechanics and the theory of operators on Hilbert space have
been deeply linked since their beginnings in the early twentieth
century. States of a quantum system correspond to certain elements of
the configuration space and observables correspond to certain
operators on the space. This book is a brief, but self-contained,
introduction to the mathematical methods of quantum mechanics, with a
view towards applications to Schrödinger operators.

Part 1 of the book is a concise introduction to the spectral theory
of unbounded operators. Only those topics that will be needed for
later applications are covered. The spectral theorem is a central
topic in this approach and is introduced at an early stage. Part 2
starts with the free Schrödinger equation and computes the free
resolvent and time evolution. Position, momentum, and angular momentum
are discussed via algebraic methods. Various mathematical methods are
developed, which are then used to compute the spectrum of the hydrogen
atom. Further topics include the nondegeneracy of the ground state,
spectra of atoms, and scattering theory.

This book serves as a self-contained introduction to spectral
theory of unbounded operators in Hilbert space with full proofs and
minimal prerequisites: Only a solid knowledge of advanced calculus and
a one-semester introduction to complex analysis are required. In
particular, no functional analysis and no Lebesgue integration theory
are assumed. It develops the mathematical tools necessary to prove
some key results in nonrelativistic quantum mechanics.

Mathematical Methods in Quantum Mechanics is intended for
beginning graduate students in both mathematics and physics and
provides a solid foundation for reading more advanced books and
current research literature.

This new edition has additions and improvements throughout the book
to make the presentation more student friendly.

The book is written in a very clear and compact style. It is well suited for self-study and includes numerous exercises (many with hints).

—Zentralblatt MATH

The author presents this material in a very clear and detailed way and supplements it by numerous exercises. This makes the book a nice introduction to this exciting field of mathematics.

—Mathematical Reviews

#### Table of Contents

# Table of Contents

## Mathematical Methods in Quantum Mechanics: With Applications to Schrodinger Operators, Second Edition

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface xi12 free
- Part 0. Preliminaries 116 free
- Chapter 0. A first look at Banach and Hilbert spaces 318
- Part 1. Mathematical foundations of quantum mechanics 4156
- Chapter 1. Hilbert spaces 4358
- Chapter 2. Self-adjointness and spectrum 6378
- Chapter 3. The spectral theorem 99114
- Chapter 4. Applications of the spectral theorem 131146
- Chapter 5. Quantum dynamics 145160
- Chapter 6. Perturbation theory for self-adjoint operators 157172
- Part 2. Schrödinger operators 185200
- Chapter 7. The free Schrödinger operator 187202
- Chapter 8. Algebraic methods 207222
- Chapter 9. One-dimensional Schrödinger operators 217232
- Chapter 10. One-particle Schrödinger operators 257272
- Chapter 11. Atomic Schrödinger operators 275290
- Chapter 12. Scattering theory 283298
- Part 3. Appendix 293308
- Chapter 13. Almost everything about Lebesgue integration 295310
- Bibliographical notes 341356
- Bibliography 345360
- Glossary of notation 349364
- Index 353368 free
- Back Cover Back Cover1378

#### Readership

Graduate students and research mathematicians interested in spectral theory and quantum mechanics, with an emphasis on Schrödinger operators.