F. Hoevermann, H. Spohn, S. Teufel
Semiclassical limit for the Schroedinger equation with a short scale periodic potential
(65K, AMS-TeX)

ABSTRACT.  We consider the dynamics generated by the Schroedinger operator $H-\frac{1}{2}\Delta + V(x) + W(\epsi x)$, where $V$ is a lattice periodic potential and $W$ an external potential which varies slowly on the scale set by the lattice spacing. We prove that in the limit $\epsi\to 0$ the time dependent position operator and, more generally, semiclassical obsevables converge strongly to a limit which is determined by the semiclassical dynamics.