Mathematical Methods in Quantum Mechanics: With Applications to Schrodinger Operators (Graduate Studies in Mathematics) 2nd Edition by Gerald Teschl (PDF)

Description

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 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.

User’s Reviews

Editorial Reviews: Review 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 MATHThe 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 ReviewsThe 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 About the Author Gerald Teschl, University of Vienna, Austria.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I am just a ‚hobby mathematician, so please consider this when you read my comments. Also this was only my second book on the subject so I do not have much to compare.I guess, a good background in complex analysis is probably sufficient, as the author provides two chapters on Banach/Hilbert spaces and on integration theory.Broadly the first 2/3 of the book were relatively easy for me to understand. The proofs of the theorems were such that I could understand them.This changed in the last 1/3 of the book. The ‚jumps‘ form one statement to the next seemed to become very large, at least for me. Statement such as ‚…as can be seem easily…‘ became more frequent.As the 2/3 of the book I understood was really very interesting, I assume someone, whose mathematical ability will be good enough for the whole book, will find it very good and very interesting.

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