{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/28693"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/28693","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Semiclassical Scattering for Two and Three Body Systems","abstract":"Semiclassical scattering theory can be summarized as the study of connections between classical mechanics and quantum mechanics in the limit ℏ → 0 over the infinite time domain -∞ < t < ∞. After a brief discussion of Semiclassical Analysis and Scattering Theory we provide a rigorous result concerning the time propogation of a semiclassical wavepacket over the time domain -∞ < t < ∞. This result has long been known for dimension n ≥ 3, and we extend it to one and two space dimensions. Next, we present a brief mathematical discussion of the three body problem, first in classical mechanics and then in quantum mechanics. Finally using an approach similar to the semiclassical wave-packet construction we form a semiclassical approximation to the solution of the Schrödinger equation for the three-body problem over the time domain -∞ < t < ∞. This technique accounts for clustering at infinite times and should be applicable for researchers studying simple recombination problems from quantum chemistry.","abstract_html":"Semiclassical scattering theory can be summarized as the study of connections between classical mechanics and quantum mechanics in the limit ℏ → 0 over the infinite time domain -∞ &lt; t &lt; ∞. After a brief discussion of Semiclassical Analysis and Scattering Theory we provide a rigorous result concerning the time propogation of a semiclassical wavepacket over the time domain -∞ &lt; t &lt; ∞. This result has long been known for dimension n ≥ 3, and we extend it to one and two space dimensions. Next, we present a brief mathematical discussion of the three body problem, first in classical mechanics and then in quantum mechanics. Finally using an approach similar to the semiclassical wave-packet construction we form a semiclassical approximation to the solution of the Schrödinger equation for the three-body problem over the time domain -∞ &lt; t &lt; ∞. This technique accounts for clustering at infinite times and should be applicable for researchers studying simple recombination problems from quantum chemistry.","abstract_has_math":false,"creators":["Rothstein, Ivan"],"institution":"Virginia Tech","degree_name":"Ph. 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After a brief discussion of Semiclassical Analysis and Scattering Theory we provide a rigorous result concerning the time propogation of a semiclassical wavepacket over the time domain -∞ < t < ∞. This result has long been known for dimension n ≥ 3, and we extend it to one and two space dimensions. Next, we present a brief mathematical discussion of the three body problem, first in classical mechanics and then in quantum mechanics. Finally using an approach similar to the semiclassical wave-packet construction we form a semiclassical approximation to the solution of the Schrödinger equation for the three-body problem over the time domain -∞ < t < ∞. This technique accounts for clustering at infinite times and should be applicable for researchers studying simple recombination problems from quantum chemistry."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:title","label":"Title","values":["Semiclassical Scattering for Two and Three Body Systems"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Hagedorn, George A."],"dc:contributor.committeemember":["Greenberg, William","Klaus, Martin","Schmittmann, Beate","Ball, Joseph A."],"dc:contributor.department":["Mathematics"],"dc:creator":["Rothstein, Ivan"],"dc:date.accessioned":["2014-03-14T20:15:20Z"],"dc:date.available":["2014-03-14T20:15:20Z","2004-08-20"],"dc:date.issued":["2004-08-12"],"dc:description.abstract":["Semiclassical scattering theory can be summarized as the study of connections between classical mechanics and quantum mechanics in the limit ℏ → 0 over the infinite time domain -∞ < t < ∞. After a brief discussion of Semiclassical Analysis and Scattering Theory we provide a rigorous result concerning the time propogation of a semiclassical wavepacket over the time domain -∞ < t < ∞. 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