#### Date of Award

1981

#### Degree Type

Dissertation

#### Degree Name

Ph.D.

#### Department

Physics

#### Keywords

Physics, General.

#### Rights

CC BY-NC-ND 4.0

#### Abstract

A variational discrete representation of the relativistic energy spectrum of an electron in a Coulomb field is constructed. It is shown that by a proper choice of the variational basis set, the eigenvalues satisfy a generalized Hylleraas-Undheim theorem. A number of relativistic sum rules which can be evaluated exactly are calculated by means of the basis set to demonstrate that the variational solutions obtained by the diagonalization of the Dirac Hamiltonian with a Coulomb potential yield a discrete representation of the hydrogenic spectrum including both the positive and negative continua. The results strongly suggest that the set of relativistic variational eigenvectors and eigenvalues can be used to construct a discrete representation of the Dirac-Green's function. As applications, the relativistic basis set is used to calculate relativistic values for dipole polarizabilities, electric dipole oscillator strength sums for the ground state with and without retardation, and two-photon decay rates for the metastable 2s(, 1/2) state in hydrogenic ions. The two-photon decay rates differ from previous calculations due to the inclusion of higher order retardation corrections. Our oscillator strength sums from the ground state appear to be much more accurate than earlier calculations. The oscillator strength densities in the continuum are used to calculate photoionization cross-sections by a Stieltjes imaging technique.Dept. of Physics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1981 .G6424. Source: Dissertation Abstracts International, Volume: 42-03, Section: B, page: 1057. Thesis (Ph.D.)--University of Windsor (Canada), 1981.

#### Recommended Citation

GOLDMAN, SAMUEL PEDRO., "APPLICATION OF DISCRETE BASIS SET METHODS TO THE DIRAC EQUATION." (1981). *Electronic Theses and Dissertations*. 1196.

https://scholar.uwindsor.ca/etd/1196