Geometric Quantization and Quantum Mechanics 1. Introduction 1.1 Background 1.2 Hamiltonian dynamics 1.3 Prequantization 1.4 Representation space 1.5 Blattner Kostant Sternberg kernels 1.6 Quantization 1.7 Schrödinger representation 1.8 Other representations 1.9 Time dependent Schrödinger equation 1.10 Relativistic dynamics in an electromagnetic field 1.11 Pauli representation 2. Hamiltonian Dynamics 2.1 Poisson algebra 2.2 Local expressions 2.3 Relativistic charged particle 2.4 Non relativistic dynamics 3. Prequantization 3.1 Connections in line bundles 3.2 Prequantization line bundle 3.3 Prequantization map 4. Representation Space 4.1 Polarization 4.2 The bundle F F 4.3 Square integrable wave functions 4.4 Bohr Sommerfeld conditions 4.5 Distributional wave functions 5. Blattner Kostant Sternberg Kernels 5.1 Transverse polarizations 5.2 Strongly admissible pairs of polarizations 5.3 Metaplectic structure 5.4 Induced metaplectic structure 6. Quantization 6.1 Lifting the action of ft 6.2 Polarization preserving functions 6.3 Quantization via Blattner Kostant Sternberg kernels 6.4 Superselection rules 7. Schrödinger Representation 7.1 Single particle 7.2 System of particles 7.3 Blattner Kostant Sternberg kernels quasiclassical approximations and Feynman path integrals 8. Other Representations 8.1 Bargmann Fock representation 8.2 Harmonic oscillator energy representation 9. Time Dependent Schrödinger Equation 10. Relativistic Dynamics in An Electromagnetic Field 10.1 Relativistic quantum dynamics 10.2 Charge superselection rules 10.3 Quantization in the Kaluza theory 11. Pauli Representation for Spin 11.1 Classical model of spin 11.2 Representation space 11.3 Quantization Glossary of Notation. This book contains a revised and expanded version of the lecture notes of two seminar series given during the academic year 1976 77 at the Department of Mathematics and Statistics of the University of Calgary and in the summer of 1978 at the Institute of Theoretical Physics of the Technical University Clausthal. The aim of the seminars was to present geometric quantization from the point of view· of its applica­ tions to quantum mechanics and to introduce the quantum dynamics of various physical systems as the result of the geometric quantization of the classical dynamics of these systems. The group representation aspects of geometric quantiza­ tion as well as proofs of the existence and the uniqueness of the introduced structures can be found in the expository papers of Blattner Kostant Sternberg and Wolf and also in the references quoted in these papers. The books of Souriau (1970) and Simms and Woodhouse (1976) present the theory of geometric quantization and its relationship to quantum mech­ anics. The purpose of the present book is to complement the preceding ones by including new developments of the theory and emphasizing the computations leading to results in quantum mechanics.