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

F. Hövermann, H. Spohn, S. Teufel

Commun. Math. Phys. 215 (2001), 609-629.
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Zusammenfassung

We consider the dynamics generated by the Schrödinger operator H=-½Δ + V(x) + W(εx), 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 ε-→0 the time dependent position operator and, more generally, semiclassical observables converge strongly to a limit which is determined by the semiclassical dynamics.