  This paper begins with some background information and a summary of results
in atomic supersymmetry. The connection between the supersymmetric Coulomb and
oscillator problems in arbitrary dimensions is outlined. Next, I treat the
issue of finding a description of supersymmetry-based quantum-defect theory in
terms of oscillators. A model with an anharmonic term that yields analytical
eigenfunctions is introduced to solve this problem in arbitrary dimensions.
Finally, I show that geonium atoms (particles contained in a Penning trap)
offer a realization of a multidimensional harmonic oscillator in an idealized
limit. The anharmonic theory presented here provides a means of modeling the
realistic case.
