Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

First Advisor

A. Ravi Prakash Rau


Two different non-separable problems are explored and analyzed. Non-perturbative methods need to be used to handle them, as the competing forces involved in these problems are equally strong and do not yield to a perturbative analysis. The first one is the study of doubly excited ridge states of atoms, in which two electrons are comparably excited. An analytical wavefunction for such states is introduced and is used to solve the two-electron Hamiltonian in the pair coordinates called "hyperspherical coordinates" variationally. The correlation between the electrons is built in analytically into the structure of the wavefunction. Sequences of ridge states out to very high excitation are computed and are organized as Rydberg series converging to the double ionization limit. Numerical results of such states in He and H$\sp-$ are compared with other theoretical calculations where available. The second problem is the analysis of the photodetachment of negative ions in an electric field via the frame transformation theory. The presence of the electric field requires a transformation from spherical to cylindrical symmetry for the outgoing photoelectron. This gives an oscillatory modulating factor as the effect of the electric field on cross-sections. All of this work is derived analytically in a general form applicable to the photodetachment of any negative ion. The expressions are applied to H$\sp-$ and S$\sp-$ for illustration.