{"id":{"repo_id":"potsdam-diss","oai_identifier":"oai:kobv.de-opus4-uni-potsdam:1093"},"canonical_url":"https://search.dev.ndltd.org/etd/potsdam-diss/oai:kobv.de-opus4-uni-potsdam:1093","repository":{"repo_id":"potsdam-diss","name":"Universität Potsdam - Diss","base_url":"https://publishup.uni-potsdam.de/opus4-ubp/oai"},"display":{"title":"Semiclassical asymptotics for the scattering amplitude in the presence of focal points at infinity","abstract":"We consider scattering in $\\R^n$, $n\\ge 2$, described by the Schr\\\"odinger operator $P(h)=-h^2\\Delta+V$, where $V$ is a short-range potential. With the aid of Maslov theory, we give a geometrical formula for the semiclassical asymptotics as $h\\to 0$ of the scattering amplitude $f(\\omega_-,\\omega_+;\\lambda,h)$ $\\omega_+\\neq\\omega_-$) which remains valid in the presence of focal points at infinity (caustics). Crucial for this analysis are precise estimates on the asymptotics of the classical phase trajectories and the relationship between caustics in euclidean phase space and caustics at infinity.","abstract_html":"We consider scattering in <span class=\"etd-inline-math\">\\R<sup>n</sup></span>, $n\\ge 2$, described by the Schr\\&quot;odinger operator <span class=\"etd-inline-math\">P(h)=-h<sup>2</sup>\\Delta+V</span>, where $V$ is a short-range potential. With the aid of Maslov theory, we give a geometrical formula for the semiclassical asymptotics as $h\\to 0$ of the scattering amplitude <span class=\"etd-inline-math\">f(&omega;<sub>-</sub>,&omega;<sub>+</sub>;\\lambda,h)</span> <span class=\"etd-inline-math\">&omega;<sub>+</sub>\\neq&omega;<sub>-</sub></span>) which remains valid in the presence of focal points at infinity (caustics). Crucial for this analysis are precise estimates on the asymptotics of the classical phase trajectories and the relationship between caustics in euclidean phase space and caustics at infinity.","abstract_has_math":true,"creators":["Hohberger, Horst"],"institution":"Universität Potsdam","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Klein, Markus"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2006,"date_issued":"2006-12-19","date_published":"2006-12-19","updated_at":"2026-07-24T03:51:20Z","subjects":["Semiklassik","mathematics","physics","scattering theory","semiclassics","scattering amplitude"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://publishup.uni-potsdam.de/frontdoor/index/index/docId/1093","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Klein, Markus"]},{"key":"dc:creator","label":"Author","values":["Hohberger, Horst"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universität Potsdam"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Potsdam"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Semiklassik","mathematics","physics","scattering theory","semiclassics","scattering amplitude"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We consider scattering in $\\R^n$, $n\\ge 2$, described by the Schr\\\"odinger operator $P(h)=-h^2\\Delta+V$, where $V$ is a short-range potential. With the aid of Maslov theory, we give a geometrical formula for the semiclassical asymptotics as $h\\to 0$ of the scattering amplitude $f(\\omega_-,\\omega_+;\\lambda,h)$ $\\omega_+\\neq\\omega_-$) which remains valid in the presence of focal points at infinity (caustics). Crucial for this analysis are precise estimates on the asymptotics of the classical phase trajectories and the relationship between caustics in euclidean phase space and caustics at infinity.","Wir betrachten Streuung in $\\R^n$, $n\\ge 2$, beschrieben durch den Schr\\\"odinger operator $P(h)=-h^2\\Delta+V$, wo $V$ ein kurzreichweitiges Potential ist. Mit Hilfe von Maslov Theorie erhalten wir eine geometrische Formel fuer die semiklassische Asymptotik ($h\\to 0$) der Streuamplitude $f(\\omega_-,\\omega_+;\\lambda,h)$ ($\\omega_+\\neq\\omega_-$) welche auch bei Vorhandensein von Fokalpunkten bei Unendlich (Kaustiken) gueltig bleibt."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Semiclassical asymptotics for the scattering amplitude in the presence of focal points at infinity","Semiklassische Asymptotik der Streuamplitude bei unendlich fernen Fokalpunkten"]}]}],"canonical_facts":{"dc:contributor":["Klein, Markus"],"dc:creator":["Hohberger, Horst"],"dc:description.abstract":["We consider scattering in $\\R^n$, $n\\ge 2$, described by the Schr\\\"odinger operator $P(h)=-h^2\\Delta+V$, where $V$ is a short-range potential. With the aid of Maslov theory, we give a geometrical formula for the semiclassical asymptotics as $h\\to 0$ of the scattering amplitude $f(\\omega_-,\\omega_+;\\lambda,h)$ $\\omega_+\\neq\\omega_-$) which remains valid in the presence of focal points at infinity (caustics). Crucial for this analysis are precise estimates on the asymptotics of the classical phase trajectories and the relationship between caustics in euclidean phase space and caustics at infinity.","Wir betrachten Streuung in $\\R^n$, $n\\ge 2$, beschrieben durch den Schr\\\"odinger operator $P(h)=-h^2\\Delta+V$, wo $V$ ein kurzreichweitiges Potential ist. Mit Hilfe von Maslov Theorie erhalten wir eine geometrische Formel fuer die semiklassische Asymptotik ($h\\to 0$) der Streuamplitude $f(\\omega_-,\\omega_+;\\lambda,h)$ ($\\omega_+\\neq\\omega_-$) welche auch bei Vorhandensein von Fokalpunkten bei Unendlich (Kaustiken) gueltig bleibt."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universität Potsdam"],"dc:subject":["Semiklassik","mathematics","physics","scattering theory","semiclassics","scattering amplitude"],"dc:title":["Semiclassical asymptotics for the scattering amplitude in the presence of focal points at infinity","Semiklassische Asymptotik der Streuamplitude bei unendlich fernen Fokalpunkten"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Potsdam"]},"updated_at":"2026-07-24T03:51:20Z"}