Branch-point structure and energy level calculations of diamagnetic hydrogen using dimensional perturbation theory.

Abstract

This dissertation describes the results of research that covers two distinct areas relevant to the field of physics: atomic theory and applied numerical analysis. In the first phase of this research the avoided crossings of diamagnetic hydrogen were examined with dimensional perturbation theory, resulting in a systematic means of understanding the appearance of these avoided crossings and where they will occur in the energy spectrum. In the second phase of this research we turned our attention to the field of approximation theory, developing a more accurate technique for summing divergent perturbation series at specific values of the independent variable. The two phases of research were finally related by applying this new technique to the diamagnetic hydrogen problem, with improved convergence and accuracy when summing the perturbation energy series.