Contents
Preface xi
Chapter 1. Introduction 1
§1.1. Basic themes 1
§1.2. Classical and quantum mechanics 3
§1.3. Overview 5
§1.4. Notes 9
Part 1. BASIC THEORY
Chapter 2. Symplectic geometry and analysis 13
§2.1. Flows 13
§2.2. Symplectic structure on
R2n
14
§2.3. Symplectic mappings 16
§2.4. Hamiltonian vector fields 20
§2.5. Lagrangian submanifolds 23
§2.6. Notes 26
Chapter 3. Fourier transform, stationary phase 27
§3.1. Fourier transform on S 27
§3.2. Fourier transform on S 35
§3.3. Semiclassical Fourier transform 38
§3.4. Stationary phase in one dimension 40
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