Abstract
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}.
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