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

The relation between the perturbed Coulomb problem in N dimensionsand the s extic anharmonic oscillator in N' dimensionsis presented and generalized in this work.We show that by performing a transformation, containing a free p arameter, on the equations for the two problems we can relate the two syste ms in dimensions that have not been previously linked. Exact solutions can be obtained for the N-dimensional systems from knownthree-dimensional solut ions of the two problems. Using the known ground-state wave functions for t hese systems, we construct supersymmetric partner potentials that allow us to apply the supersymmetric large-Nexpansion to obtain accurate approximate energy eigenvalues.