The eigenvalues of the potentials ${\mathit{V}}_1$(r)=-a/r+br+${\mathit{cr}}^2$ and ${\mathit{V}}_2$(r)=μ${\mathit{r}}^2$+λ${\mathit{r}}^4$+η${\mathit{r}}^6$ are obtained in N-dimensional space by the infinite Hill determinant method for a wide range of values of the parameters. We discuss the explicit dependence of these two potentials in higher-dimensional space. By using the formalism of supersymmetric quantum mechanics, it is shown that exact solutions of these potentials exist when the parameters satisfy certain constraints.

• Received 17 February 1995

DOI:https://doi.org/10.1103/PhysRevA.52.1850