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Dispersive Properties of Schrödinger Equations


Cai, Kaihua (2005) Dispersive Properties of Schrödinger Equations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/EGNB-FZ41.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Dispersive; Schrodinger
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Schlag, Wilhelm
Thesis Committee:
  • Schlag, Wilhelm (chair)
  • Pramanik, Malabika
  • Goldberg, Michael
  • Killip, Rowan
Defense Date:19 May 2005
Record Number:CaltechETD:etd-06022005-153453
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2392
Deposited By: Imported from ETD-db
Deposited On:03 Jun 2005
Last Modified:10 Dec 2020 20:16

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