Semiclassical limit for the Schrodinger equation with a short scale periodic potential

We consider the dynamics generated by the Schrodinger operator H = -1/2 Delta + V(x) + W (epsilonx), 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 epsilon --> 0 the time dependent position operator and, more generally, semiclassical observables converge strongly to a limit which is determined by the semiclassical dynamics.