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

Details Semiclassical limit for the Schroedinger equation with a short scale periodic potential Semiclassical limit for the Schroedinger equation with a short scale periodic potential

2000-01-31

arxiv.org/abs/math-ph/0001042v1

Commun.Math.Phys., Vol. 215, Issue 3, 609-629 (2001).

Physics

Mathematical Physics

Scientific paper

10.1007/s002200000314

We consider the dynamics generated by the Schroedinger operator $H=-{1/2}\Delta + V(x) + W(\epsi x)$, 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 observables converge strongly to a limit which is determined by the semiclassical dynamics.

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