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Twisted pseudodifferential calculus and application to the quantum evolution of molecules


About this Title

André Martinez and Vania Sordoni

Publication: Memoirs of the American Mathematical Society
Publication Year 2009: Volume 200, Number 936
ISBNs: 978-0-8218-4296-6 (print); 978-1-4704-0550-2 (online)
DOI: http://dx.doi.org/10.1090/memo/0936
MathSciNet review: 2527490
MSC (2000): Primary 35Q40; Secondary 35S05, 47G30, 47N50, 81Q20, 81V55

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Table of Contents


Chapters

  • Chapter 1. Introduction
  • Chapter 2. Assumptions and main results
  • Chapter 3. A modified operator
  • Chapter 4. Twisted -admissible operators
  • Chapter 5. Twisted partial differential operators
  • Chapter 6. Construction of a quasi-invariant subspace
  • Chapter 7. Decomposition of the evolution for the modified operator
  • Chapter 8. Proof of Theorem 2.1
  • Chapter 9. Proof of Corollary 2.6
  • Chapter 10. Computing the effective Hamiltonian
  • Chapter 11. Propagation of wave-packets
  • Chapter 12. Application to polyatomic molecules
  • Appendix A. Smooth pseudodifferential calculus with operator-valued symbol
  • Appendix B. Propagation of the support
  • Appendix C. Two technical lemmas