On the relationship between anharmonic oscillators and perturbed Coulomb potentials in N dimensions

The relation between the perturbed Coulomb problem in N dimensions and the sextic anharmonic oscillator in Nʹ dimensions is presented and generalized in this work. We show that by performing a transformation, containing a free parameter, on the equations for the two problems we can relate the two systems in dimensions that have not been previously linked. Exact solutions can be obtained for the N -dimensional systems from known three-dimensional solutions of the two problems. Using the known ground-state wave functions for these systems, we construct supersymmetric partner potentials that allow us to apply the supersymmetric large-N expansion to obtain accurate approximate energy eigenvalues.