The semiclassical limit of quantum dynamics

dc.contributor.authorRobinson, Sam Leslieen
dc.contributor.committeechairHagedorn, George A.en
dc.contributor.committeechairBall, Joseph A.en
dc.contributor.committeechairKohler, Werner E.en
dc.contributor.committeechairSlawny, Josephen
dc.contributor.committeechairZweifel, Paul F.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2017-03-10T21:54:35Zen
dc.date.available2017-03-10T21:54:35Zen
dc.date.issued1986en
dc.description.abstractWe study the ħ→0 limit of the quantum dynamics determined by the Hamiltonian H(ħ) = -(ħ²/2m)Δ + V on L²(ℝ<sup>n</sup>) for a large class of potentials. By convolving with certain Gaussian states we obtain classically determined asymptotic behavior of the quantum evolution of states of compact support. For suitable potentials we obtain the analogus result for the scattering operator in the position representation. For initial or incoming states of class C<sub>o</sub>¹ the error terms are shown to have L² norms of order ħ<sup>½-ε</sup> for arbitrarily small positive ε.en
dc.description.degreePh. D.en
dc.format.extentv, 69 leavesen
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/10919/76489en
dc.language.isoen_USen
dc.publisherVirginia Polytechnic Institute and State Universityen
dc.relation.isformatofOCLC# 14471546en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1986.R624en
dc.subject.lcshQuantum theoryen
dc.subject.lcshScattering (Mathematics)en
dc.titleThe semiclassical limit of quantum dynamicsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en
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