Hydrogenic atoms in the external potential V(r)=gr+λr²: exact solutions and ground-state eigenvalue bounds using moment methods

An infinite number of exact solutions for the ground and excited states of an s-wave hydrogenic atom with the perturbation V(r)= gr+ lambda r² are constructed, subject to special relations between g, lambda and the nuclear charge Z. A powerful method of Stieltjes moments is employed to generate rapidly converging upper and lower bounds to the ground-state energy E₀(Z, g, lambda ) for arbitrary g, Z and positive lambda . The accuracies of these bounds are relatively insensitive to the strength of the perturbation. The moment method also generates the exact s-wave ground-state solutions mentioned above.