The Book
Semiclassical 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.
The Author(s)
Maciej Zworski is Professor of Mathematics at the University of California, Berkeley, USA.
Table of Contents
Preface
Chapter 1. Introduction
Part 1. BASIC THEORY
Chapter 2. Symplectic geometry and analysis
Chapter 3. Fourier transform, stationary phase
Chapter 4. Semiclassical quantization
Part 2. APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS
Chapter 5. Semiclassical defect measures
Chapter 6. Eigenvalues and eigenfunctions
Chapter 7. Estimates for solutions of PDE
Part 3. ADVANCED THEORY AND APPLICATIONS
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
Part 4. SEMICLASSICAL ANALYSIS ON MANIFOLDS
Chapter 14. Manifolds
Chapter 15. Quantum ergodicity
Part 5. APPENDICES
Appendix A. Notation
Appendix B. Differential forms
Appendix C. Functional analysis
Appendix D. Fredholm theory
Bibliography
Index