Dispersive properties of Schrodinger equations

Dispersive;Schrodinger

Cai, Kaihua

University:California Institute of Technology

关键词: Dispersive;    Schrodinger;   

Others  :  https://thesis.library.caltech.edu/2392/1/thesis.pdf

美国|英语

来源: Caltech THESIS

【 摘 要 】

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}.