Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Quantum Mechanics for Mathematicians
 
Leon A. Takhtajan Stony Brook University, Stony Brook, NY
Quantum Mechanics for Mathematicians
Quantum Mechanics for Mathematicians
Hardcover ISBN:  978-0-8218-4630-8
Product Code:  GSM/95
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-1162-6
Product Code:  GSM/95.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-0-8218-4630-8
eBook: ISBN:  978-1-4704-1162-6
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
Quantum Mechanics for Mathematicians
Click above image for expanded view
Quantum Mechanics for Mathematicians
Quantum Mechanics for Mathematicians
Leon A. Takhtajan Stony Brook University, Stony Brook, NY
Hardcover ISBN:  978-0-8218-4630-8
Product Code:  GSM/95
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-1162-6
Product Code:  GSM/95.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-0-8218-4630-8
eBook ISBN:  978-1-4704-1162-6
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
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 952008; 387 pp
    MSC: Primary 81;

    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-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis.

    Readership

    Graduate 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
  • Reviews
     
     
    • ...heaven-sent 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 Babes-Bolyai, Mathematica
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 952008; 387 pp
MSC: Primary 81;

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-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis.

Readership

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
  • ...heaven-sent 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 Babes-Bolyai, Mathematica
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.