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The Born-Oppenheimer approximation in scattering theory

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dc.contributor.authorKargol, Arminen
dc.contributor.committeechairHagedorn, George A.en
dc.contributor.committeememberBowden, Robert L.en
dc.contributor.committeememberKlaus, Martinen
dc.contributor.committeememberSlawny, Josephen
dc.contributor.committeememberZweifel, Paul F.en
dc.contributor.departmentMathematical Physicsen
dc.date.accessioned2014-03-14T21:09:54Zen
dc.date.adate2006-03-02en
dc.date.available2014-03-14T21:09:54Zen
dc.date.issued1994-05-05en
dc.date.rdate2006-03-02en
dc.date.sdate2006-03-02en
dc.description.abstractWe analyze the Schrödinger equation i𝜖 ¬<sup>2</sup>â /â tΨ = H(𝜖)Ψ, where H(â ¬) = - f24 Î x + h(X) is the hamiltonian of a molecular system consisting of nuclei with masses of order 𝜖¬<sup>-4</sup> and electrons with masses of order 1. The Born-Oppenheimer approximation consists of the adiabatic approximation to the motion of electrons and the semiclassical approximation to the time evolution of nuclei. The quantum propagator associated with this Schrödinger Equation is exp(-itH(â ¬)/â ¬<sup>2</sup>). We use the Born-Oppenheimer method to find the leading order asymptotic expansion in â ¬ to exp(_it~(t:»Ψ, i.e., we find Ψ(t) such that: (1) We show that if H(𝜖) describes a diatomic Molecule with smooth short range potentials, then the estimate (1) is uniform in time; hence the leading order approximation to the wave operators can be constructed. We also comment on the generalization of our method to polyatomic molecules and to Coulomb systems.en
dc.description.degreePh. D.en
dc.format.extentv, 77 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-03022006-093405en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-03022006-093405/en
dc.identifier.urihttp://hdl.handle.net/10919/37449en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1994.K3734.pdfen
dc.relation.isformatofOCLC# 31183670en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1994.K3734en
dc.subject.lcshBorn approximationen
dc.titleThe Born-Oppenheimer approximation in scattering theoryen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematical Physicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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