Two Approximate Analytic Eigensolutions of the Hellmann Potential with any Arbitrary Angular Momentum

The parametric Nikiforov-Uvarov (pNU) and asymptotic iteration method (AIM) are applied to study the approximate analytic bound state eigensolutions (energy levels and wave functions) of the radial Schrodinger equation (SE) for the Hellmann potential which represents the superposition of the attractive Coulomb potential (-a/r) and the Yukawa potential b exp(-delta r)/r of arbitrary strength b and screening parameter delta in closed form. The analytical expressions to the energy eigenvalues E-nl yield quite accurate results for a wide range of n,l in the limit of very weak screening but the results become gradually worse as the strength b and the screening coefficient delta increase. The calculated bound state energies have been compared with available numerical data. Special cases of our solution like pure Coulomb and Yukawa potentials are also investigated.