Semiclassical limit for the Schroedinger equation with a short scale periodic potential
Hoevermann, F. ; Spohn, H. ; Teufel, S.
arXiv, 0001042 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2000-01-31
Classification:  Mathematical Physics 
@article{0001042,
     author = {Hoevermann, F. and Spohn, H. and Teufel, S.},
     title = {Semiclassical limit for the Schroedinger equation with a short scale
  periodic potential},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0001042}
}

Hoevermann, F.; Spohn, H.; Teufel, S. Semiclassical limit for the Schroedinger equation with a short scale
  periodic potential. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0001042/