Mathematical Methods in Quantum Mechanics With Applications to Schrodinger Operators

Teschl, Gerald

ISBN 10: 1470417049 / ISBN 13: 9781470417048

Published by Amer Mathematical Society, 2014

2nd edition. 358 pages. 10.50x7.00x1.00 inches. In Stock. Seller Inventory # __1470417049

Synopsis:

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.

About the Author: Gerald Teschl, University of Vienna, Austria.

Bibliographic Details

Title: Mathematical Methods in Quantum Mechanics ...
Publisher: Amer Mathematical Society
Publication Date: 2014
Binding: Hardcover
Condition: Brand New
Edition: 2nd Edition