From the reviews of the second edition: "Just as the general theory of relativity leads to many new mathematical advances and applications, the same is true of quantum mechanics. It is these mathematical advances that are the topic of this extensive volume, a volume which also delineates how these advances made possible the difficult transition from understanding hydrogen to understanding complex atoms, molecules, and 'large systems'. As such this volume will serve as an excellent source book for the mathematical basis of the many recent advances in quantum mechanics. It will also serve as an excellent text book for an advanced course in either quantum physics or applied mathematics." (Physicalia, 25/3, 2003) "This work is written uncompromisingly for the mathematical physicist ... . Thirring writes concisely but with a clarity that makes the book easy to read. ... There are extensive bibliographies, with references mostly to articles in journals ... . There are copious problems and-even better-all the solutions. ... the volume would make a valuable addition to the library of ... a mathematical physicist." (Prof. A.I. Solomon, Contemporary Physics, Vol. 46 (4), 2005) "This volume will serve as an excellent source book for the mathematical basis of the many recent advances in quantum mechanics. It will also serve as an excellent textbook ... . Each chapter is chock full of mathematical derivations and proofs but perhaps the most interesting part of each proof is the following section entitled 'Remarks' sections which are full of interesting details, ideas, drawbacks, comments, and references. ... As is usually the case with Springer-Verlag, this book has been beautifully produced ... ." (Fernande Grandjean and Gary J. Long, Physicalia, Vol. 25 (3), 2003)
