Eigenvalues of anharmonic oscillators and the perturbed Coulomb problem in<i>N</i>-dimensional space

Abstract

The eigenvalues of the potentials ${\mathit{V}}_{1}$(r)=-a/r+br+${\mathit{cr}}^{2}$ and ${\mathit{V}}_{2}$(r)=\ensuremath{\mu}${\mathit{r}}^{2}$+\ensuremath{\lambda}${\mathit{r}}^{4}$+\ensuremath{\eta}${\mathit{r}}^{6}$ 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.