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Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations
 
Ping Zhang Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People’s Republic of China
A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University
Front Cover for Wigner Measure and Semiclassical Limits of Nonlinear Schrodinger Equations
Available Formats:
Softcover ISBN: 978-0-8218-4701-5
Product Code: CLN/17
197 pp 
List Price: $35.00
MAA Member Price: $31.50
AMS Member Price: $28.00
Electronic ISBN: 978-1-4704-3117-4
Product Code: CLN/17.E
197 pp 
List Price: $33.00
MAA Member Price: $29.70
AMS Member Price: $26.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $52.50
MAA Member Price: $47.25
AMS Member Price: $42.00
Front Cover for Wigner Measure and Semiclassical Limits of Nonlinear Schrodinger Equations
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  • Front Cover for Wigner Measure and Semiclassical Limits of Nonlinear Schrodinger Equations
  • Back Cover for Wigner Measure and Semiclassical Limits of Nonlinear Schrodinger Equations
Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations
Ping Zhang Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People’s Republic of China
A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University
Available Formats:
Softcover ISBN:  978-0-8218-4701-5
Product Code:  CLN/17
197 pp 
List Price: $35.00
MAA Member Price: $31.50
AMS Member Price: $28.00
Electronic ISBN:  978-1-4704-3117-4
Product Code:  CLN/17.E
197 pp 
List Price: $33.00
MAA Member Price: $29.70
AMS Member Price: $26.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $52.50
MAA Member Price: $47.25
AMS Member Price: $42.00
  • Book Details
     
     
    Courant Lecture Notes
    Volume: 172008
    MSC: Primary 35;

    This book is based on a course entitled “Wigner measures and semiclassical limits of nonlinear Schrödinger equations,” which the author taught at the Courant Institute of Mathematical Sciences at New York University in the spring of 2007. The author's main purpose is to apply the theory of semiclassical pseudodifferential operators to the study of various high-frequency limits of equations from quantum mechanics. In particular, the focus of attention is on Wigner measure and recent progress on how to use it as a tool to study various problems arising from semiclassical limits of Schrödinger-type equations.

    At the end of each chapter, the reader will find references and remarks about recent progress on related problems. The book is self-contained and is suitable for an advanced graduate course on the topic.

    Readership

    Graduate students and research mathematicians interested in PDE's of Schrödinger and kinetic type.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. The classical WKB method
    • Chapter 2. Wigner measure
    • Chapter 3. The limit from the one-dimensional Schrödinger-Poisson to Vlasov-Poisson equations
    • Chapter 4. Semiclassical limit of Schrödinger-Poisson equations
    • Chapter 5. Semiclassical limit of the cubic Schrödinger equation in an exterior domain
    • Chapter 6. Incompressible and compressible limits of coupled systems of nonlinear Schrödinger equations
    • Chapter 7. High-frequency limit of the Helmholtz equation
    • Appendix A. Global solutions to (3.14)
    • Appendix B. Denseness of polynomials
    • Appendix C. Global existence of a solution to (5.1)
    • Appendix D. Global smooth solution to (6.1)
  • Request Review Copy
Volume: 172008
MSC: Primary 35;

This book is based on a course entitled “Wigner measures and semiclassical limits of nonlinear Schrödinger equations,” which the author taught at the Courant Institute of Mathematical Sciences at New York University in the spring of 2007. The author's main purpose is to apply the theory of semiclassical pseudodifferential operators to the study of various high-frequency limits of equations from quantum mechanics. In particular, the focus of attention is on Wigner measure and recent progress on how to use it as a tool to study various problems arising from semiclassical limits of Schrödinger-type equations.

At the end of each chapter, the reader will find references and remarks about recent progress on related problems. The book is self-contained and is suitable for an advanced graduate course on the topic.

Readership

Graduate students and research mathematicians interested in PDE's of Schrödinger and kinetic type.

  • Chapters
  • Chapter 1. The classical WKB method
  • Chapter 2. Wigner measure
  • Chapter 3. The limit from the one-dimensional Schrödinger-Poisson to Vlasov-Poisson equations
  • Chapter 4. Semiclassical limit of Schrödinger-Poisson equations
  • Chapter 5. Semiclassical limit of the cubic Schrödinger equation in an exterior domain
  • Chapter 6. Incompressible and compressible limits of coupled systems of nonlinear Schrödinger equations
  • Chapter 7. High-frequency limit of the Helmholtz equation
  • Appendix A. Global solutions to (3.14)
  • Appendix B. Denseness of polynomials
  • Appendix C. Global existence of a solution to (5.1)
  • Appendix D. Global smooth solution to (6.1)
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