Toward a Rigorous Justification of the Three-Body Impact Parameter Approximation

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dc.contributor.authorBowman, Adamen
dc.contributor.committeechairHagedorn, George A.en
dc.contributor.committeememberKlaus, Martinen
dc.contributor.committeememberBall, Joseph A.en
dc.contributor.committeememberElgart, Alexanderen
dc.contributor.departmentMathematicsen
dc.date.accessioned2015-09-21T12:32:09Zen
dc.date.available2015-09-21T12:32:09Zen
dc.date.issued2014-03-06en
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
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.othervt_gsexam:2347en
dc.identifier.urihttp://hdl.handle.net/10919/56623en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectScattering Theoryen
dc.subjectStationary Phaseen
dc.subjectQuantum Mechanicsen
dc.subjectImpact Parameter Approximationen
dc.subjectCharge Transfer Modelen
dc.subjectDyson Seriesen
dc.titleToward a Rigorous Justification of the Three-Body Impact Parameter Approximationen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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