Time-Dependent Perturbation and the Born-Oppenheimer Approximation

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dc.contributor.authorJilcott, Steven Wayne Jr.en
dc.contributor.committeechairHagedorn, George A.en
dc.contributor.committeememberChang, Lay Namen
dc.contributor.committeememberKohler, Werner E.en
dc.contributor.committeememberKlaus, Martinen
dc.contributor.committeememberBeattie, Christopher A.en
dc.contributor.departmentPhysicsen
dc.date.accessioned2014-03-14T20:09:30Zen
dc.date.adate2000-04-13en
dc.date.available2014-03-14T20:09:30Zen
dc.date.issued2000-03-09en
dc.date.rdate2001-04-13en
dc.date.sdate2000-04-13en
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.en
dc.description.degreePh. D.en
dc.identifier.otheretd-04132000-13040037en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04132000-13040037/en
dc.identifier.urihttp://hdl.handle.net/10919/26814en
dc.publisherVirginia Techen
dc.relation.haspartetd.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectmoleculesen
dc.subjectFranck-Condon factorsen
dc.subjectelectromagnetic fielden
dc.subjectperturbation theoryen
dc.subjectlaseren
dc.subjectBorn-Oppenheimer approximationen
dc.titleTime-Dependent Perturbation and the Born-Oppenheimer Approximationen
dc.typeDissertationen
thesis.degree.disciplinePhysicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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