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A Riemann-Hilbert approach to scattering on a one-dimensional semi-infinite crystal

by Darryl V Johnson

Institution:	University of Tennessee Chattanooga
Department:
Degree:
Year:	2017
Keywords:	Riemann-Hilbert problems
Posted:	2/1/2018 12:00:00 AM
Record ID:	2151584
Full text PDF:	https://scholar.utc.edu/theses/516

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.Advisors/Committee Members: Belinskiy, Boris, Nichols, Roger, Ledoan, Andrew, Kong, Lingju, College of Arts and Sciences.