Mathematical Methods in Quantum Mechanics: With Applications to Schrodinger Operators

by Gerald Teschi

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 Schrodinger 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 Schrodinger 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 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. It is well suited for self-study and includes numerous exercises (many with hints).

Genres: Mathematics, Physics, Quantum Mechanics

305 pages, Hardcover

First published January 1, 2009

Reviews

[Kevin K. Gillette · Rating 5 out of 5]

I saw this book in a list of recommended titles following the purchase of another volume on quantum mechanics, and thought, "Why not?" I was very pleasantly surprised to see how accessible it turns out to be! I would recommend this book for anyone looking to drop into the lively art and science of quantum mechanical calculations, which are essential to gaining an understanding of what quantum mechanics is. Very readable and well-developed with the intelligent beginner in mind.