Quantum Mechanics for Mathematicians

by Leon A. Takhtajan

Takhtadzhian, also spelled Takhtajan, (mathematics, Stony Brook U.) offers a textbook based on a course he has long taught to second year graduates of mathematics who were assumed to have no prior knowledge of physics. He introduces the basic concepts and methods of quantum mechanics, emphasizing those aspects that have influenced the recent course of mathematics in the same manner that classical physics did from the 17th to the 19th centuries. The material can be used for a one-year course or two one-semester courses. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)

Genres: Physics, Mathematics, Quantum Mechanics, Science

387 pages, Hardcover

First published August 15, 2008

Reviews

[Jon Paprocki · Rating 4 out of 5]

This is an excellent book to read if you want to put all of the quantum mechanics you learned in a physics class on a rigorous basis, which is precisely what it sets out to do. The final chapter on supersymmetry is a must-read if you've ever wondered why mathematicians also care about supersymmetry, namely that somehow it is a great tool to study manifold theory. It ends with a supersymmetry proof of the Atiyah-Singer index theorem (which was my original reason to study this book), but I think reading the original papers on this topic along with the paper by Getzler making it rigorous is a better place to learn that topic from, as the proof given here is not fully rigorous and lacking detail. Some sections introduce tools and then never really explain how they are used in physics (e.g. deformation quantization), but would be fine to read side-by-side with a physicist's quantum mechanics textbook. I think it would be difficult to get the motivation to read through this book if you have no prior exposure to quantum mechanics, though. A mathematician interested in quantum mechanics might be better served by studying Griffith's quantum mechanics textbook for a couple of months to get the feel for it before diving into this book.

The textbook does not shy from making full use of advanced mathematics, including symplectic geometry, functional analysis, and Lie groups, and so a first year graduate level education in mathematics is recommended.