Dispersive properties of Schrodinger equations

by Cai, Kaihua

This thesis mainly concerns the dispersive properties of Schrodinger equations with certain potentials, and some of their consequences. First, we consider the charge transfer models in R^n with n > 2. In this case, the potential is a sum of several individual real-valued potentials, each moving with constant velocities. We get an L^1 to L^infty estimate for the evolution and the asymptotic completeness of the evoution in any Sobolev space. Second, we derive the L^1 to L^infty estimate for the Schrodinger operators with a Lame potential. The Lame potential is spatially periodic and its spectrum has the structure of finite bands. We obtain a dispersive estimate with a decay rate t^{-1/3}.