Radiation conditions for periodic potentials

by Thai Ngoc Nguyen
Doctoral thesis
Date of Examination:2017-01-27
Date of issue:2017-09-19
Advisor:Prof. Dr. Ingo Witt
Referee:Prof. Dr. Ingo Witt
Referee:PD Dr. Wolfram Bauer
Persistent Address: http://dx.doi.org/10.53846/goediss-6488

 

 

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Description:The aim of the present thesis is to determine radiation conditions for higher-dimensional Schroedinger equations with periodic potentials. There is well-known result for Helmholtz equations. However to my knowledge, there have been only a few works on periodic Schroedinger equations.

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Abstract

English

The aim of the present thesis is to determine radiation conditions for higher-dimensional Schroedinger equations with periodic potentials. There is well-known result for Helmholtz equations. However to my knowledge, there have been only a few works on periodic Schroedinger equations. We employ Floquet Bloch theory to study periodic Schroedinger operators. The limiting absorption principal derives integral formulas for solutions of periodic Schroedinger equations. Then, we use the analytic perturbation theory and the stationary phase method to establish the radiation conditions.
Keywords: Mathematics+Mathematical physics; Mathematics+Mathematical physics
 
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