Atomic Supersymmetry, Oscillators, and the Penning Trap

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.