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

Abstract

The relation between the perturbed Coulomb problem in N dimensionsand the sextic anharmonic oscillator in N' dimensionsis 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 knownthree-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-Nexpansion to obtain accurate approximate energy eigenvalues.PACS Nos.: 03.65.Ge, 03.65.Fd, 11.30.Na