Memoirs of the American Mathematical Society 2009; 82 pp; softcover Volume: 200 ISBN10: 082184296X ISBN13: 9780821842966 List Price: US$62 Individual Members: US$37.20 Institutional Members: US$49.60 Order Code: MEMO/200/936
 The authors construct an abstract pseudodifferential calculus with operatorvalued symbol, suitable for the treatment of Coulombtype interactions, and they apply it to the study of the quantum evolution of molecules in the BornOppenheimer approximation, in the case of the electronic Hamiltonian admitting a local gap in its spectrum. In particular, they show that the molecular evolution can be reduced to the one of a system of smooth semiclassical operators, the symbol of which can be computed explicitely. In addition, they study the propagation of certain wave packets up to long time values of Ehrenfest order. Table of Contents  Introduction
 Assumptions and main results
 A modified operator
 Twisted \(h\)admissible operators
 Twisted partial differential operators
 Construction of a quasiinvariant subspace
 Decomposition of the evolution for the modified operator
 Proof of Theorem 2.1
 Proof of Corollary 2.6
 Computing the effective Hamiltonian
 Propagation of wavepackets
 Application to polyatomic molecules
 Appendix A. Smooth pseudodifferential calculus with operatorvalued symbol
 Appendix B. Propagation of the support
 Appendix C. Two technical lemmas
 Appendix. Bibliography
