Eigenvalues of anharmonic oscillators and the perturbed Coulomb problem inN-dimensional space

The eigenvalues of the potentials V₁(r)=-a/r+br+cr² and V₂(r)={μ}r²+{λ}r⁴+{η}r⁶ 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.