{"id":{"repo_id":"utc","oai_identifier":"oai:scholar.utc.edu:theses-1653"},"canonical_url":"https://search.dev.ndltd.org/etd/utc/oai:scholar.utc.edu:theses-1653","repository":{"repo_id":"utc","name":"University of Tennessee - Chattanooga","base_url":"https://scholar.utc.edu/do/oai/"},"display":{"title":"A Riemann-Hilbert approach to scattering on a one-dimensional semi-infinite crystal","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Johnson, Darryl V."],"institution":"University of Tennessee at Chattanooga","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Belinskiy, Boris","Nichols, Roger; Ledoan, Andrew; Kong, Lingju","College of Arts and Sciences"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T05:46:51Z","subjects":["Riemann-Hilbert problems"],"languages":["English","eng"],"rights":[],"rights_urls":["https://rightsstatements.org/page/InC/1.0/?language=en"],"identifier_entries":[]},"links":{"outbound_url":"https://scholar.utc.edu/theses/516","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Belinskiy, Boris","Nichols, Roger; Ledoan, Andrew; Kong, Lingju","College of Arts and Sciences"]},{"key":"dc:creator","label":"Author","values":["Johnson, Darryl V."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-05-01T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"]},{"key":"dc:relation","label":"Dc Relation","values":["Masters Theses and Doctoral Dissertations"]},{"key":"dc:type","label":"Dc Type","values":["Masters theses","Text"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Riemann-Hilbert problems"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["https://rightsstatements.org/page/InC/1.0/?language=en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholar.utc.edu/theses/516"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Dept. of Mathematics","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."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["A Riemann-Hilbert approach to scattering on a one-dimensional semi-infinite crystal"]}]}],"canonical_facts":{"dc:contributor":["Belinskiy, Boris","Nichols, Roger; Ledoan, Andrew; Kong, Lingju","College of Arts and Sciences"],"dc:creator":["Johnson, Darryl V."],"dc:date":["2017-05-01T07:00:00Z"],"dc:description":["Dept. of Mathematics","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."],"dc:description.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."],"dc:identifier":["https://scholar.utc.edu/theses/516"],"dc:language":["English","eng"],"dc:publisher":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"],"dc:relation":["Masters Theses and Doctoral Dissertations"],"dc:rights":["https://rightsstatements.org/page/InC/1.0/?language=en"],"dc:subject":["Riemann-Hilbert problems"],"dc:title":["A Riemann-Hilbert approach to scattering on a one-dimensional semi-infinite crystal"],"dc:type":["Masters theses","Text"]},"updated_at":"2026-07-24T05:46:51Z"}