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Hardcover ISBN:  9780821846308 
Product Code:  GSM/95 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Sale Price:  $87.75 
eBook ISBN:  9781470411626 
Product Code:  GSM/95.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Sale Price:  $55.25 
Hardcover ISBN:  9780821846308 
eBook ISBN:  9781470411626 
Product Code:  GSM/95.B 
List Price:  $220.00$177.50 
MAA Member Price:  $198.00$159.75 
AMS Member Price:  $176.00$142.00 
Sale Price:  $143.00$115.38 

Book DetailsGraduate Studies in MathematicsVolume: 95; 2008; 387 ppMSC: Primary 81;
This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with secondyear 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 AtiyahSinger 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 firstyear graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis.ReadershipGraduate students and research mathematicians interested in mathematical aspects of quantum mechanics.

Table of Contents

Part 1. Foundations

Chapter 1. Classical mechanics

Chapter 2. Basic principles of quantum mechanics

Chapter 3. Schrödinger equation

Chapter 4. Spin and identical particles

Part 2. Functional methods and supersymmetry

Chapter 5. Path integral formulation of quantum mechanics

Chapter 6. Integration in functional spaces

Chapter 7. Fermion systems

Chapter 8. Supersymmetry


Additional Material

Reviews

...heavensent to the aforementioned analytic number theorist, i.e., me, because it is mathematics, not physics: the exposition is peppered with definitions and theorems, and proofs!, proofs!, proofs!...
Michael Berg for MAA Reviews 
By a clever selection of the material and the clear way of exposing it, the book is recommended for graduate students in mathematics looking for applications in physics, as well as for student in physics desiring to be acquainted, in a rigorous but, at the same time, quick and accessible manner, with the basic mathematical tools used in quantum mathematics.
Studia Universitatis BabesBolyai, Mathematica


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This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with secondyear 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 AtiyahSinger 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 firstyear graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis.
Graduate students and research mathematicians interested in mathematical aspects of quantum mechanics.

Part 1. Foundations

Chapter 1. Classical mechanics

Chapter 2. Basic principles of quantum mechanics

Chapter 3. Schrödinger equation

Chapter 4. Spin and identical particles

Part 2. Functional methods and supersymmetry

Chapter 5. Path integral formulation of quantum mechanics

Chapter 6. Integration in functional spaces

Chapter 7. Fermion systems

Chapter 8. Supersymmetry

...heavensent to the aforementioned analytic number theorist, i.e., me, because it is mathematics, not physics: the exposition is peppered with definitions and theorems, and proofs!, proofs!, proofs!...
Michael Berg for MAA Reviews 
By a clever selection of the material and the clear way of exposing it, the book is recommended for graduate students in mathematics looking for applications in physics, as well as for student in physics desiring to be acquainted, in a rigorous but, at the same time, quick and accessible manner, with the basic mathematical tools used in quantum mathematics.
Studia Universitatis BabesBolyai, Mathematica