Title page for ETD etd-042399-105022


Type of Document Dissertation
Author Marmorino, Matthew G.
URN etd-042399-105022
Title Lower bounds to eigenvalues by the method of arbitrary choice without truncation
Degree PhD
Department Chemistry
Advisory Committee
Advisor Name Title
Schug, John C. Committee Chair
Beattie, Christopher A. Committee Member
Heflin, James R. Committee Member
Marand, Hervé L. Committee Member
Viers, Jimmy W. Committee Member
Keywords
  • eigenvalues
  • variation theorem
  • hylleraas
  • united atom
  • lower bounds
Date of Defense 1999-04-21
Availability mixed
Abstract

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.

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