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

### About this Title

**Gerald Teschl**, *University of Vienna, Vienna, Austria*

Publication: Graduate Studies in Mathematics

Publication Year
2009: Volume 99

ISBNs: 978-0-8218-4660-5 (print); 978-1-4704-1838-0 (online)

DOI: http://dx.doi.org/10.1090/gsm/099

MathSciNet review: MR2499016

MSC: Primary 81-01; Secondary 47N50, 81Qxx

### Table of Contents

**Front/Back Matter**

**Part 0. Preliminaries **

- Chapter 0. A first look at Banach and Hilbert spaces

**Part 1. Mathematical foundations of quantum mechanics **

- Chapter 1. Hilbert spaces
- Chapter 2. Self-adjointness and spectrum
- Chapter 3. The spectral theorem
- Chapter 4. Applications of the spectral theorem
- Chapter 5. Quantum dynamics
- Chapter 6. Perturbation theory for self-adjoint operators

**Part 2. Schrödinger operators **

- Chapter 7. The free Schrödinger operator
- Chapter 8. Algebraic methods
- Chapter 9. One dimensional Schrödinger operators
- Chapter 10. One-particle Schrödinger operators
- Chapter 11. Atomic Schrödinger operators
- Chapter 12. Scattering theory

**Part 3. Appendix **

- Appendix A. Almost everything about Lebesgue integration