2012 Young Researchers Workshop:
Kinetic Description of Multiscale Phenomena

semiclassical limit of Schrodinger equation with periodic potential, and band-crossing

Qin Li

University of Wisconsin-Madison

In this talk, I will present the semi-classical limit of Schrodinger equation whose periodic potential oscillate in the scale of Planck constant. Correspondance of Bloch eigen-functions on the phase space will be given too. In case eigenmodes get close or even degenerate, where band-crossing takes place, we set up fine mesh to study details of the crossing, while away from the degenerate point, weak limit were adopted.