Committee Chair

Belinskiy, Boris

Committee Member

Nichols, Roger; Ledoan, Andrew; Kong, Lingju

Department

Dept. of Mathematics

College

College of Arts and Sciences

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

In this paper the scattering of a non-relativistic particle on a semi-infinite crystal is analyzed using the method of the Riemann-Hilbert Problem for analytic functions. We proceed in the framework of the limiting absorption principle. Our formulas allow to find the scattered field at any point of the crystal. In particular, we obtain an explicit formula for the reflection coefficient off the crystal. We discuss the limiting cases of the strong and weak potentials. For compactly supported potentials we present a general result regarding a relation between the reflection and transmission coefficients.

Degree

M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science.

Date

5-2017

Subject

Riemann-Hilbert problems

Keyword

Riemann-Hilbert; Scattering; Semi-infinite crystal; Limiting absorption principle

Document Type

Masters theses

Extent

v, 34 leaves

Language

English

Rights

Under copyright.

License

http://creativecommons.org/licenses/by-nc-nd/3.0/

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