Hövermann, Frank; Spohn, Herbert; Teufel, Stefan Semiclassical limit for the Schrödinger equation with a short scale periodic potential. (English) Zbl 1052.81039 Commun. Math. Phys. 215, No. 3, 609-629 (2001). In this paper, the dynamics generated by the time Schrodinger equation with the potential consisting of a lattice periodic potential plus an external potential which varies slowly on the scale of the lattice spacing is investigated. Theorems proved in this paper show that for very slow changes of the external potential the time position operator and, more generally, semiclassical observables converge to a limit given by the semiclassical dynamics. Results are given for isolated bands only (no band crossing is considered). Reviewer: Lubomír Skála (Praha) Cited in 13 Documents MSC: 81Q99 General mathematical topics and methods in quantum theory 35J10 Schrödinger operator, Schrödinger equation 46N50 Applications of functional analysis in quantum physics 47N50 Applications of operator theory in the physical sciences 82B99 Equilibrium statistical mechanics Keywords:time Schrödinger equation; semiclassical limit PDFBibTeX XMLCite \textit{F. Hövermann} et al., Commun. Math. Phys. 215, No. 3, 609--629 (2001; Zbl 1052.81039) Full Text: DOI arXiv