Mathematical Methods in Quantum Mechanics

With Applications to Schrodinger Operators

Gerald Teschl (Autor)

Buch | Hardcover

356 Seiten

2014 | Second Edition
American Mathematical Society (Verlag)
978-1-4704-1704-8 (ISBN)

Artikel merken

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.

Gerald Teschl, University of Vienna, Austria.

Preface
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
Chapter 13. Almost everything about Lebesgue integration
Bibliographical notes
Bibliography
Glossary of notation
Index

Reihe/Serie	Graduate Studies in Mathematics
Verlagsort	Providence
Sprache	englisch
Maße	152 x 229 mm
Gewicht	809 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
ISBN-10	1-4704-1704-9 / 1470417049
ISBN-13	978-1-4704-1704-8 / 9781470417048
Zustand	Neuware