Quantum Mechanics for Mathematicians
This book is, in a sense, a continuation of the book by L. D. Fadeev and O. A. Yakubovskii, which is also reviewed in this issue of the newsletter. Both books are based on courses given to mathematically oriented students with the aim of describing basic ideas, fact and tools from quantum physics. This book covers a broader array of topics, including more advanced ones. In the first part, the author reviews the main facts of classical mechanics, introduces the basic principles of quantum mechanics and describes the Schrödinger equation (including a description of the hydrogen atom and the first part of a discussion of semi-classical asymptotics). This part ends with a discussion of particles with spin and systems of identical particles. The second part starts with a description of the Feynman path formulation of quantum mechanics (also containing a discussion of regularized determinants of differential operators and a further discussion of semi-classical asymptotics). The next chapter treats Gaussian and Wiener measures and the Gaussian Wiener integral. A description of fermionic systems using Grassmann algebras, graded linear algebra and path integrals for anticommuting variables then leads naturally to an introduction to supermanifolds and supersymmetry. The book is an excellent introduction to quantum physics both for students of mathematics and for mathematicians wanting to learn basic facts from quantum mechanics and quantum field theory in the language of mathematics.