Abstract
dc:description.abstractSemiclassical 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.
Degree
thesis:*- Name thesis:degree_name
- Ph. D.
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 2004
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Rothstein, Ivan
- Chair dc:contributor.committeechair
-
- Hagedorn, George A.
- Committee members dc:contributor.committeemember
-
- Greenberg, William
- Klaus, Martin
- Schmittmann, Beate
- Ball, Joseph A.
Subjects
dc:subject × 2Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-08172004-122051
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/28693