Semiclassical Analysis

Maciej Zworski

• Publisher: American Mathematical Society
• Year: 2012
• Print ISBN:
  9781470470623
• eBook ISBN:
  9780821889954
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

This book is an excellent, comprehensive introduction to semiclassical analysis. I believe it will become a standard reference for the subject.—Alejandro Uribe, University of MichiganSemiclassical analysis provides PDE techniques based on the classical-quantum (particle-wave) correspondence. These techniques include such well-known tools as geometric optics and the Wentzel–Kramers–Brillouin approximation. Examples of problems studied in this subject are high energy eigenvalue asymptotics and effective dynamics for solutions of evolution equations. From the mathematical point of view, semiclassical analysis is a branch of microlocal analysis which, broadly speaking, applies harmonic analysis and symplectic geometry to the study of linear and nonlinear PDE. The book is intended to be a graduate level text introducing readers to semiclassical and microlocal methods in PDE. It is augmented in later chapters with many specialized advanced topics which provide a link to current research literature.

Table of contents

• Cover
• Title page
• Contents
• Preface
• Chapter 1. Introduction
• Chapter 2. Symplectic geometry and analysis
• Chapter 3. Fourier transform, stationary phase
• Chapter 4. Semiclassical quantization
• Chapter 5. Semiclassical defect measures
• Chapter 6. Eigenvalues and eigenfunctions
• Chapter 7. Estimates for solutions of PDE
• Chapter 8. More on the symbol calculus
• Chapter 9. Changing variables
• Chapter 10. Fourier integral operators
• Chapter 11. Quantum and classical dynamics
• Chapter 12. Normal forms
• Chapter 13. The FBI transform
• Chapter 14. Manifolds
• Chapter 15. Quantum ergodicity
• Appendix A. Notation
• Appendix B. Differential forms
• Appendix C. Functional analysis
• Appendix D. Fredholm theory
• Bibliography
• Index
• Back Cover