{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/36249"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/36249","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"The Born-Oppenheimer Approximation for Triatomic Molecules with Large Angular Momentum in Two Dimensions","abstract":"We study the Born-Oppenheimer approximation for a symmetric linear triatomic molecule in two space dimensions. We compute energy levels up to errors of order ε⁵, uniformly for three bounded vibrational quantum numbers n₁, n₂, and n₃; and nuclear angular momentum quantum numbers â ≤ kε<sup>-3/4</sup> for k > 0. Here the small parameter ε is the fourth root of the ratio of the electron mass to an average nuclear mass.","abstract_html":"We study the Born-Oppenheimer approximation for a symmetric linear triatomic molecule in two space dimensions. We compute energy levels up to errors of order ε⁵, uniformly for three bounded vibrational quantum numbers n₁, n₂, and n₃; and nuclear angular momentum quantum numbers â ≤ kε&lt;sup&gt;-3/4&lt;/sup&gt; for k &gt; 0. Here the small parameter ε is the fourth root of the ratio of the electron mass to an average nuclear mass.","abstract_has_math":false,"creators":["Bowman, Adam Shoresworth"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Hagedorn, George A."],"committee_members":["Valeyev, Eduard Faritovich","Elgart, Alexander"],"year":2010,"date_issued":"2010-12-08","date_published":"2010-12-08","updated_at":"2026-07-22T22:18:49Z","subjects":["Born-Oppenheimer","Triatomic Molecules","Multiple Scales"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-12172010-164613"],"render_values":[{"text":"etd-12172010-164613","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/36249","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Hagedorn, George A."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Valeyev, Eduard Faritovich","Elgart, Alexander"]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Bowman, Adam Shoresworth"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:50:12Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:50:12Z","2011-01-12"]},{"key":"dc:date.issued","label":"Date","values":["2010-12-08"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Born-Oppenheimer","Triatomic Molecules","Multiple Scales"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-12172010-164613"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/36249"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We study the Born-Oppenheimer approximation for a symmetric linear triatomic molecule in two space dimensions. We compute energy levels up to errors of order ε⁵, uniformly for three bounded vibrational quantum numbers n₁, n₂, and n₃; and nuclear angular momentum quantum numbers â ≤ kε<sup>-3/4</sup> for k > 0. Here the small parameter ε is the fourth root of the ratio of the electron mass to an average nuclear mass."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["The Born-Oppenheimer Approximation for Triatomic Molecules with Large Angular Momentum in Two Dimensions"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Hagedorn, George A."],"dc:contributor.committeemember":["Valeyev, Eduard Faritovich","Elgart, Alexander"],"dc:contributor.department":["Mathematics"],"dc:creator":["Bowman, Adam Shoresworth"],"dc:date.accessioned":["2014-03-14T20:50:12Z"],"dc:date.available":["2014-03-14T20:50:12Z","2011-01-12"],"dc:date.issued":["2010-12-08"],"dc:description.abstract":["We study the Born-Oppenheimer approximation for a symmetric linear triatomic molecule in two space dimensions. We compute energy levels up to errors of order ε⁵, uniformly for three bounded vibrational quantum numbers n₁, n₂, and n₃; and nuclear angular momentum quantum numbers â ≤ kε<sup>-3/4</sup> for k > 0. Here the small parameter ε is the fourth root of the ratio of the electron mass to an average nuclear mass."],"dc:description.degree":["Master of Science"],"dc:identifier.other":["etd-12172010-164613"],"dc:identifier.uri":["http://hdl.handle.net/10919/36249"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Born-Oppenheimer","Triatomic Molecules","Multiple Scales"],"dc:title":["The Born-Oppenheimer Approximation for Triatomic Molecules with Large Angular Momentum in Two Dimensions"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:18:49Z"}