| Softcover ISBN: | 978-0-8218-4701-5 |
| Product Code: | CLN/17 |
| 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 |
| List Price: | $33.00 |
| MAA Member Price: | $29.70 |
| AMS Member Price: | $26.40 |
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Book DetailsCourant Lecture NotesVolume: 17; 2008; 197 ppMSC: 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.ReadershipGraduate students and research mathematicians interested in PDE's of Schrödinger and kinetic type.
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Table of Contents
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Chapters
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Chapter 1. The classical WKB method
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Chapter 2. Wigner measure
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Chapter 3. The limit from the one-dimensional Schrödinger-Poisson to Vlasov-Poisson equations
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Chapter 4. Semiclassical limit of Schrödinger-Poisson equations
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Chapter 5. Semiclassical limit of the cubic Schrödinger equation in an exterior domain
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Chapter 6. Incompressible and compressible limits of coupled systems of nonlinear Schrödinger equations
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Chapter 7. High-frequency limit of the Helmholtz equation
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Appendix A. Global solutions to (3.14)
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Appendix B. Denseness of polynomials
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Appendix C. Global existence of a solution to (5.1)
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Appendix D. Global smooth solution to (6.1)
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Additional Material
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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.
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
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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)
