Memoirs of the American Mathematical Society Twisted Pseudodifferential Calculus and Application to Quantum Evolution Molecules

Constructs an abstract pseudodifferential calculus with operator-valued symbol, suitable for the treatment of Coulomb-type interactions. This title shows that the molecular evolution can be reduced to the one of a system of smooth semiclassical operators, the symbol of which can be computed explicitly. The authors construct an abstract pseudodifferential calculus with operator-valued symbol, suitable for the treatment of Coulomb-type interactions, and they apply it to the study of the quantum evolution of molecules in the Born-Oppenheimer 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 explicitly. In addition, they study the propagation of certain wave packets up to long time values of Ehrenfest order.