Quantum Mechanics for Mathematicians
( Graduate Studies in Mathematics )
Publication series ：Graduate Studies in Mathematics
Author： Leon A. Takhtajan
Publisher： American Mathematical Society
Publication year： 2008
E-ISBN: 9781470411626
P-ISBN(Hardback): 9780821846308
Subject： O413.1 quantum mechanics (wave mechanics, matrix mechanics)
Keyword： 暂无分类
Language： ENG
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Quantum Mechanics for Mathematicians
Description
This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. In addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrödinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks and in specialized literature. This book is written in a concise style with careful attention to precise mathematics formulation of methods and results. Numerous problems, from routine to advanced, help the reader to master the subject. In addition to providing a fundamental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory. Prerequisites include standard first-ye
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