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University of Tennessee at Chattanooga
A Riemann-Hilbert approach to scattering on a one-dimensional semi-infinite crystal
Abstract
dc:description.abstractIn 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
thesis:*- Grantor dc:publisher
- University of Tennessee at Chattanooga
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Johnson, Darryl V.
- Contributors dc:contributor
-
- Belinskiy, Boris
- Nichols, Roger; Ledoan, Andrew; Kong, Lingju
- College of Arts and Sciences
Subjects
dc:subject × 1Rights
dc:rights- Language dc:language
- English, eng
Identifiers
dc:identifier.*- Repository record dc:identifier
- https://scholar.utc.edu/theses/516
- OAI identifier oai:identifier
- oai:scholar.utc.edu:theses-1653