Dispersive Properties of Schrödinger Equations

Author: Cai, Kaihua

Year: 2005

Degree: Dissertation (Ph.D.)

Advisor: Schlag, Wilhelm

Committee Members: Schlag, Wilhelm; Pramanik, Malabika; Goldberg, Michael; Killip, Rowan

Option: Mathematics

DOI: 10.7907/EGNB-FZ41

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 Rn 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 L1 to L∞ estimate for the evolution and the asymptotic completeness of the evolution in any Sobolev space.

Second, we derive the L1 to L∞ 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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