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

After 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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Chemistry

Department dc:contributor.department

Chemistry

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1999

Author dc:creator

• Marmorino, Matthew G.

Chair dc:contributor.committeechair

• Schug, John C.

Committee members dc:contributor.committeemember

• Heflin, James R.
• Marand, Hervé L.
• Beattie, Christopher A.
• Viers, Jimmy W.

• eigenvalues
• variation theorem
• hylleraas
• united atom
• lower bounds

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en_US

Dc Identifier Other

etd-042399-105022

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/79725