Hydrogenic energy levels in two dimensions at arbitrary magnetic fields

Abstract

The eigenvalue spectrum for a hydrogenic potential [V(r)=-${e}^{2}$/r] in two dimensions is studied for perpendicular magnetic fields of arbitrary strength. The weak-field regime has been treated by considering the magnetic field as a perturbation while in the strong-field regime the potential is treated as a perturbation. A two-point Pad\'e approximant is shown to provide a reliable interpolation between these two limiting situations, allowing us to present accurate analytic expressions for the magnetic-field dependence of both ground- and excited-state energies.