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dc.contributor.authorBowman, Adamen_US
dc.date.accessioned2015-09-21T12:32:09Z
dc.date.available2015-09-21T12:32:09Z
dc.date.issued2014-03-06en_US
dc.identifier.othervt_gsexam:2347en_US
dc.identifier.urihttp://hdl.handle.net/10919/56623
dc.description.abstractThe impact parameter (IP) approximation is a semiclassical model in quantum scattering theory wherein N large masses interact with one small mass. We study this model in one spatial dimension using the tools of time-dependent scattering theory, considering a system of two large-mass particles and one small-mass particle. We demonstrate that the model's predictive power becomes arbitrarily good as the masses of the two heavy particles are made larger by studying the S-matrix for a particular scattering channel. We also show that the IP wave functions can be made arbitrarily close to the full three-body solution, uniformly in time, provided one of the large masses is fixed in place, and that such a result probably will not hold if we allow all the masses to move.en_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThis Item is protected by copyright and/or related rights. Some uses of this Item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subjectScattering Theoryen_US
dc.subjectStationary Phaseen_US
dc.subjectQuantum Mechanicsen_US
dc.subjectImpact Parameter Approximationen_US
dc.subjectCharge Transfer Modelen_US
dc.subjectDyson Seriesen_US
dc.titleToward a Rigorous Justification of the Three-Body Impact Parameter Approximationen_US
dc.typeDissertationen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairHagedorn, George A.en_US
dc.contributor.committeememberKlaus, Martinen_US
dc.contributor.committeememberBall, Joseph A.en_US
dc.contributor.committeememberElgart, Alexanderen_US


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