{"id":{"repo_id":"toronto-retro","oai_identifier":"oai:utoronto.scholaris.ca:1807/140728"},"canonical_url":"https://search.dev.ndltd.org/etd/toronto-retro/oai:utoronto.scholaris.ca:1807/140728","repository":{"repo_id":"toronto-retro","name":"University of Toronto","base_url":"https://utoronto.scholaris.ca/server/oai/request"},"display":{"title":"On Adiabatic Quantum Molecular Dynamics","abstract":"In this thesis, we consider the time-dependent Born-Oppenheimer approximation (BOA) of a non-relativistic quantum molecule involving a possibly large number of nuclei and electrons described by the Schrödinger equation. The full molecular equation is difficult to solve and compute approximations for due to the highly oscillatory nature of the solutions in space and time and due to the high dimensionality of the state space. In the spirit of Born and Oppenheimer, we study quantitatively the approximation of the molecular evolution. We obtain an iterable approximation of the molecular evolution to arbitrary order and we derive an effective equation for the reduced dynamics involving the nuclei, equivalent to the original Schrödinger equation and containing no electron variables (thus reducing the large state space of the full evolution). We estimate the coefficients of the new equation and find tractable approximations for it.","abstract_html":"In this thesis, we consider the time-dependent Born-Oppenheimer approximation (BOA) of a non-relativistic quantum molecule involving a possibly large number of nuclei and electrons described by the Schrödinger equation. The full molecular equation is difficult to solve and compute approximations for due to the highly oscillatory nature of the solutions in space and time and due to the high dimensionality of the state space. In the spirit of Born and Oppenheimer, we study quantitatively the approximation of the molecular evolution. We obtain an iterable approximation of the molecular evolution to arbitrary order and we derive an effective equation for the reduced dynamics involving the nuclei, equivalent to the original Schrödinger equation and containing no electron variables (thus reducing the large state space of the full evolution). We estimate the coefficients of the new equation and find tractable approximations for it.","abstract_has_math":false,"creators":["Gherghe, Sebastian Tudor"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Mathematics","school":null,"contributors":[],"advisors":["Sigal, Israel M"],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-11","date_published":"2024-11","updated_at":"2026-07-27T21:27:52Z","subjects":["Adiabatic","Born Oppenheimer","Molecular dynamics","Quantum mechanics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1807/140728","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Sigal, Israel M"]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Gherghe, Sebastian Tudor"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2024-11"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-11-13T17:08:55Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-11-13T17:08:55Z"]},{"key":"dc:date.issued","label":"Date","values":["2024-11"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Adiabatic","Born Oppenheimer","Molecular dynamics","Quantum mechanics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1807/140728"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we consider the time-dependent Born-Oppenheimer approximation (BOA) of a non-relativistic quantum molecule involving a possibly large number of nuclei and electrons described by the Schrödinger equation. The full molecular equation is difficult to solve and compute approximations for due to the highly oscillatory nature of the solutions in space and time and due to the high dimensionality of the state space. In the spirit of Born and Oppenheimer, we study quantitatively the approximation of the molecular evolution. We obtain an iterable approximation of the molecular evolution to arbitrary order and we derive an effective equation for the reduced dynamics involving the nuclei, equivalent to the original Schrödinger equation and containing no electron variables (thus reducing the large state space of the full evolution). We estimate the coefficients of the new equation and find tractable approximations for it."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["On Adiabatic Quantum Molecular Dynamics"]}]}],"canonical_facts":{"dc:contributor.advisor":["Sigal, Israel M"],"dc:contributor.department":["Mathematics"],"dc:creator":["Gherghe, Sebastian Tudor"],"dc:date":["2024-11"],"dc:date.accessioned":["2024-11-13T17:08:55Z"],"dc:date.available":["2024-11-13T17:08:55Z"],"dc:date.issued":["2024-11"],"dc:description.abstract":["In this thesis, we consider the time-dependent Born-Oppenheimer approximation (BOA) of a non-relativistic quantum molecule involving a possibly large number of nuclei and electrons described by the Schrödinger equation. The full molecular equation is difficult to solve and compute approximations for due to the highly oscillatory nature of the solutions in space and time and due to the high dimensionality of the state space. In the spirit of Born and Oppenheimer, we study quantitatively the approximation of the molecular evolution. We obtain an iterable approximation of the molecular evolution to arbitrary order and we derive an effective equation for the reduced dynamics involving the nuclei, equivalent to the original Schrödinger equation and containing no electron variables (thus reducing the large state space of the full evolution). We estimate the coefficients of the new equation and find tractable approximations for it."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["http://hdl.handle.net/1807/140728"],"dc:subject":["Adiabatic","Born Oppenheimer","Molecular dynamics","Quantum mechanics"],"dc:title":["On Adiabatic Quantum Molecular Dynamics"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T21:27:52Z"}