Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations ( Courant Lecture Notes )

Publication series ：Courant Lecture Notes

Author： Ping Zhang  

Publisher： American Mathematical Society‎

Publication year： 2008

E-ISBN: 9781470431174

P-ISBN(Hardback):  9780821847015

Subject： O413.1 quantum mechanics (wave mechanics, matrix mechanics)

Keyword： 暂无分类

Language： ENG

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Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations

Description

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.

Chapter

Cover

General editor information

Title page

Contents

Preface

The classical WKB method

Wigner measure

The limit from the one-dimensional Schrödinger-Poisson to Vlasov-Poisson equations

Semiclassical limit of Schrödinger-Poisson equations

Semiclassical limit of the cubic Schrödinger equation in an exterior domain

Incompressible and compressible limits of coupled systems of nonlinear Schrödinger equations

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)

Bibliography

Back Cover

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