Journal of Mathematical Chemistry

, Volume 49, Issue 8, pp 1535–1543

Eigenvalue lower bounds with Bazley’s special choice of an infinite-dimensional subspace

Original Paper

DOI: 10.1007/s10910-011-9839-y

Cite this article as:
Marmorino, M.G. J Math Chem (2011) 49: 1535. doi:10.1007/s10910-011-9839-y

Abstract

Bazley’s special choice of a finite-dimensional space to construct an intermediate operator between a base operator and the full Hamiltonian is a standard technique to calculate lower bounds to the energies of a system. We modify Bazley’s method to accommodate an infinite-dimensional space that is complete in one particle of the system. An application to the helium atom shows improvement in the lower bound to the ground-state energy, indicating promise in our method. However, significant problems are revealed which include (1) poorer bounds for the excited states, (2) lack of symmetry in the intermediate operator, and (3) lack of direction for improvement.

Keywords

Lower bounds Bazley Special choice Helium 

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Chemistry and BiochemistryIndiana University South BendSouth BendUSA