Description

Foreword.- Preface.- Prologue.- Part I: Symplectic Mechanics.- 1. Hamiltonian Mechanics in a Nutshell.- 2. The Symplectic Group.- 3. Free Symplectic Matrices.- 4. The Group of Hamiltonian Symplectomorphisms.- 5. Symplectic Capacities.- 6. Uncertainty Principles.- Part II: Harmonic Analysis in Symplectic Spaces.- 7. The Metaplectic Group.- 8. Heisenberg-Weyl and Grossmann-Royer Operators.- 9. Cross-ambiguity and Wigner Functions.- 10. The Weyl Correspondence.- 11. Coherent States and Anti-Wick Quantization.- 12. Hilbert-Schmidt and Trace Class Operators.- 13. Density Operator and Quantum States.- Part III: Pseudo-differential Operators and Function Spaces.- 14. Shubin's Global Operator Calculus.- Part IV: Applications.- 15. The Schrödinger Equation.- 16. The Feichtinger Algebra.- 17. The Modulation Spaces M^q_s.- 18. Bopp Pseudo-differential Operators.- 19. Applications of Bopp Quantization.- Bibliography.- Index.