Homer L. Dodge Department
of Physics and Astronomy
The University of Oklahoma

My group is engaged in the study of fundamental quantum mechanical questions for both simple atomic systems such as helium and most recently for Bose-Einstein condensates. Specifically, we are trying to address these questions using a method called dimensional perturbation theory, in which the Schrödinger equation is solved in an arbitrary number of dimensions. Our philosophy stems from the notion that, just as the two-dimensional world is easier to understand from the perspective of three dimensions, so we believe that we can gain insight into our three-dimensional world using the perspective of higher dimensions. We are presently pursuing several studies, including a detailed look at states of helium as a function of dimension D including the group-theoretic basis for inter-dimensional degeneracies, a study of diamagnetic hydrogen including Rydberg states, and an analysis of properties of Bose-Einstein condensates using trap parameters that approximate current experimental conditions at various laboratories. Our Bose-Einstein work is exploring ways to go beyond the mean field approximation, known as the Gross-Pitaevskii equation, to bring in many-body effects.

Dimensional perturbation theory has thus far been the source of some surprising insight into the dynamics of few-body systems, including electron geometry, classification of doubly-excited states, patterns in helium spectra, and should provide a unique vantage point from which to analyze Bose-Einstein condensation.

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