New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education
 Graduate Studies in Mathematics 2014; 356 pp; hardcover Volume: 157 ISBN-10: 1-4704-1704-9 ISBN-13: 978-1-4704-1704-8 List Price: US$67 Member Price: US$53.60 Order Code: GSM/157 Not yet published.Expected publication date is November 3, 2014. See also: Jacobi Operators and Completely Integrable Nonlinear Lattices - Gerald Teschl Ordinary Differential Equations and Dynamical Systems - Gerald Teschl Spectral Analysis, Differential Equations and Mathematical Physics: A Festschrift in Honor of Fritz Gesztesy's 60th Birthday - Helge Holden, Barry Simon and 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 Readership Graduate students and research mathematicians interested in spectral theory and quantum mechanics, with an emphasis on Schrödinger operators. Table of Contents Preliminaries A first look at Banach and Hilbert spaces Mathematical foundations of quantum mechanics Hilbert spaces Self-adjointness and spectrum The spectral theorem Applications of the spectral theorem Quantum dynamics Perturbation theory for self-adjoint operators Schrödinger operators The free Schrödinger operator Algebraic methods One-dimensional Schrödinger operators One-particle Schrödinger operators Atomic Schrödinger operators Scattering theory Appendix Almost everything about Lebesgue integration Bibliographical notes Bibliography Glossary of notation Index