Lower bounds to eigenvalues by the method of arbitrary choice without truncation

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dc.contributor.authorMarmorino, Matthew G.en
dc.contributor.committeechairSchug, John C.en
dc.contributor.committeememberHeflin, James R.en
dc.contributor.committeememberMarand, Hervé L.en
dc.contributor.committeememberBeattie, Christopher A.en
dc.contributor.committeememberViers, Jimmy W.en
dc.contributor.departmentChemistryen
dc.date.accessioned2017-10-20T16:29:32Zen
dc.date.adate1999-04-30en
dc.date.available2017-10-20T16:29:32Zen
dc.date.issued1999-04-21en
dc.date.rdate1999-04-30en
dc.date.sdate1999-04-23en
dc.description.abstractAfter a detailed discussion of the variation theorem for upper bound calculation of eigenvalues, many standard procedures for determining lower bounds to eigenvalues are presented with chemical applications in mind. A new lower bound method, arbitrary choice without trunctation is presented and tested on the helium atom. This method is attractive because it does not require knowledge of the eigenvalues or eigenvectors of the base problem. In application, however, it is shown that the method is disappointing for two reasons: 1) the method does not guarantee improved bounds as calculational effort is increased; and 2) the method requires some a priori information which, in general, may not be available. A possible direction for future work is pointed out in the end. An extension of a lower bound method by Calogero and Marchioro has been developed and is presented in appendix G along with comments on the effective field method in appendix H for Virginia Tech access only.en
dc.description.degreePh. D.en
dc.description.notesTo avoid copyright infringements, access to these three appendices (G, H, and I) has been permanently limited to the Virginia Tech campus. In the case that Virginia Tech places these appendices freely on the internet, Virginia Tech is solely responsible for copyright violations.en
dc.identifier.otheretd-042399-105022en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-042399-105022/en
dc.identifier.urihttp://hdl.handle.net/10919/79725en
dc.language.isoen_USen
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjecteigenvaluesen
dc.subjectvariation theoremen
dc.subjecthylleraasen
dc.subjectunited atomen
dc.subjectlower boundsen
dc.titleLower bounds to eigenvalues by the method of arbitrary choice without truncationen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineChemistryen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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