Abstract
dc:description.abstractWe discuss the physical problem of a molecule interacting with an electromagnetic field pulse and model the problem using a time-dependent perturbation of the Born-Oppenheimer approximation to the Schrodinger equation. Using previous results that develop asymptotic series solutions in the Born-Oppenheimer parameter ε, we derive a formal Dyson series expansion in the perturbation parameter μ, which is proportional to the electromagnetic field strength. We then prove that this series is asymptotically accurate in both parameters, provided that the Hamiltonian for the electrons has purely discrete spectrum. Under more general hypotheses, we show that the series is accurate to first order in μ, and that it is accurate to one higher order if we place conditions on the abruptness of the EM pulse. We also show how this series development provides a justification for the Franck-Condon factors in the case of a diatomic molecule.
Degree
thesis:*- Name thesis:degree_name
- Ph. D.
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Physics
- Department dc:contributor.department
- Physics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 2000
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Jilcott, Steven Wayne Jr.
- Chair dc:contributor.committeechair
-
- Hagedorn, George A.
- Committee members dc:contributor.committeemember
-
- Chang, Lay Nam
- Kohler, Werner E.
- Klaus, Martin
- Beattie, Christopher A.
Subjects
dc:subject × 6Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-04132000-13040037
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/26814