Contents Chapter 1. Introduction 1 Chapter 2. Assumptions and Main Results 7 Chapter 3. A Modified Operator 13 Chapter 4. Twisted h-Admissible Operators 17 Chapter 5. Twisted Partial Differential Operators 27 Chapter 6. Construction of a Quasi-Invariant Subspace 33 Chapter 7. Decomposition of the Evolution for the Modified Operator 39 Chapter 8. Proof of Theorem 2.1 45 Chapter 9. Proof of Corollary 2.6 47 Chapter 10. Computing the Effective Hamiltonian 51 Chapter 11. Propagation of Wave-Packets 59 Chapter 12. Application to Polyatomic Molecules 65 Appendix A. Smooth Pseudodifferential Symbol 73 Appendix B. Propagation of the Support 75 Appendix C. Two Technical Lemmas 79 Appendix. Bibliography 81 v Calculus with Operator-Valued
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