Semiclassical Scattering for Two and Three Body Systems
| dc.contributor.author | Rothstein, Ivan | en |
| dc.contributor.committeechair | Hagedorn, George A. | en |
| dc.contributor.committeemember | Greenberg, William | en |
| dc.contributor.committeemember | Klaus, Martin | en |
| dc.contributor.committeemember | Schmittmann, Beate | en |
| dc.contributor.committeemember | Ball, Joseph A. | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2014-03-14T20:15:20Z | en |
| dc.date.adate | 2004-08-20 | en |
| dc.date.available | 2014-03-14T20:15:20Z | en |
| dc.date.issued | 2004-08-12 | en |
| dc.date.rdate | 2004-08-20 | en |
| dc.date.sdate | 2004-08-17 | en |
| 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 < ∞. 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. | en |
| dc.description.degree | Ph. D. | en |
| dc.identifier.other | etd-08172004-122051 | en |
| dc.identifier.sourceurl | http://scholar.lib.vt.edu/theses/available/etd-08172004-122051/ | en |
| dc.identifier.uri | http://hdl.handle.net/10919/28693 | en |
| dc.publisher | Virginia Tech | en |
| dc.relation.haspart | diss.pdf | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | Semiclassical | en |
| dc.subject | Scattering | en |
| dc.title | Semiclassical Scattering for Two and Three Body Systems | en |
| dc.type | Dissertation | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Ph. D. | en |
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