Martinez A., Sordoni V.
On the Time-Dependent Born-Oppenheimer Approximation with Smooth
Potential
(23K, LATeX)
ABSTRACT. We give a general reduction scheme for the study of the quantum
propagator of molecular Schr\"odinger operators with smooth potentials.
This reduction is made up to infinitely (resp. exponentially) small
error terms with respect to the inverse square root of the mass of the
nuclei, depending on the $C^\infty$ (resp. analytic) smoothness of the
interactions. Then we apply this result to the case when an electronic
level is isolated from the rest of the spectrum of the electronic
Hamiltonian.