Born-Oppenheimer Corrections Near a Renner-Teller Crossing

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dc.contributor.authorHerman, Mark Stevenen
dc.contributor.committeechairHagedorn, George A.en
dc.contributor.committeememberCrawford, T. Danielen
dc.contributor.committeememberKlaus, Martinen
dc.contributor.committeememberBall, Joseph A.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:13:43Zen
dc.date.adate2008-07-09en
dc.date.available2014-03-14T20:13:43Zen
dc.date.issued2008-07-03en
dc.date.rdate2008-07-09en
dc.date.sdate2008-07-03en
dc.description.abstractWe perform a rigorous mathematical analysis of the bending modes of a linear triatomic molecule that exhibits the Renner-Teller effect. Assuming the potentials are smooth, we prove that the wave functions and energy levels have asymptotic expansions in powers of ε, where ε4 is the ratio of an electron mass to the mass of a nucleus. To prove the validity of the expansion, we must prove various properties of the leading order equations and their solutions. The leading order eigenvalue problem is analyzed in terms of a parameter bË , which is equivalent to the parameter originally used by Renner. For 0 &lt bË &lt 1, we prove self-adjointness of the leading order Hamiltonian, that it has purely discrete spectrum, and that its eigenfunctions and their derivatives decay exponentially. Perturbation theory and finite difference calculations suggest that the ground bending vibrational state is involved in a level crossing near bË = 0.925. We also discuss the degeneracy of the eigenvalues. Because of the crossing, the ground state is degenerate for 0 &lt bË &lt 0.925 and non-degenerate for 0.925 &lt bË &lt 1.en
dc.description.degreePh. D.en
dc.identifier.otheretd-07032008-115546en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-07032008-115546/en
dc.identifier.urihttp://hdl.handle.net/10919/28200en
dc.publisherVirginia Techen
dc.relation.haspartMSH_Phd.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectPerturbation Theoryen
dc.subjectBorn-Oppenheimer Approximationen
dc.subjectRenner-Teller Effecten
dc.titleBorn-Oppenheimer Corrections Near a Renner-Teller Crossingen
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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