Mathematical Methods in Quantum Mechanics With Applications to Schrödinger Operators

By Gerald Teschl et al

Published on June 10, 2009

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Table of Contents

Contents
Preface xi
Part 0. Preliminaries
Chapter 0. A first look at Banach and Hilbert spaces 3
Chapter 1. Mathematical Foundations of Quantum Mechanics 37
Chapter 2. Self-adjointness and spectrum 55
Chapter 3. The spectral theorem 87
Chapter 4. Applications of the spectral theorem 111
Chapter 5. Quantum dynamics 123
Chapter 6. Perturbation theory for self-adjoint operators 133
Part 2. Schrödinger Operators
Chapter 7. The free Schrödinger operator 161
Chapter 8. Algebraic methods 173
Chapter 9. One-dimensional Schrödinger operators 181
Chapter 10. One-particle Schrödinger operators 221
Chapter 11. Atomic Schrödinger operators 239
Chapter 12. Scattering theory 247
Part 3. Appendix
Appendix A. Almost everything about Lebesgue integration 259
Bibliographical notes 289
Bibliography 293
Glossary of notation 297
Index 301

Summary

This book provides a self-contained introduction to mathematical methods in quantum mechanics (spectral theory) with applications to Schrödinger operators. It covers mathematical foundations of quantum mechanics, self-adjointness, spectral theorem, quantum dynamics, perturbation theory, Schrödinger operators, algebraic methods, one-dimensional operators, atomic operators, and scattering theory. The author, Gerald Teschl, along with others, presents a comprehensive guide suitable for graduate studies in mathematics. Published in 2009, this book is a valuable resource for those interested in quantum mechanics.