**Courant Lecture Notes**

Volume: 17;
2008;
197 pp;
Softcover

MSC: Primary 35;

Print ISBN: 978-0-8218-4701-5

Product Code: CLN/17

List Price: $33.00

Individual Member Price: $26.40

**Electronic ISBN: 978-1-4704-3117-4
Product Code: CLN/17.E**

List Price: $33.00

Individual Member Price: $26.40

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#### Supplemental Materials

# Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations

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*Ping Zhang*

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University

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.

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

#### Table of Contents

# Table of Contents

## Wigner Measure and Semiclassical Limits of Nonlinear Schrodinger Equations

- Cover Cover11
- General editor information ii3
- Title page iii4
- Contents v6
- Preface vii8
- The classical WKB method 110
- Wigner measure 1120
- The limit from the one-dimensional Schrödinger-Poisson to Vlasov-Poisson equations 3746
- Semiclassical limit of Schrödinger-Poisson equations 8190
- Semiclassical limit of the cubic Schrödinger equation in an exterior domain 105114
- Incompressible and compressible limits of coupled systems of nonlinear Schrödinger equations 129138
- High-frequency limit of the Helmholtz equation 153162
- Appendix A. Global solutions to (3.14) 173182
- Appendix B. Denseness of polynomials 177186
- Appendix C. Global existence of a solution to (5.1) 179188
- Appendix D. Global smooth solution to (6.1) 189198
- Bibliography 193202
- Back Cover Back Cover1209

#### Readership

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