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

Abstract

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 Schr¨odinger equation (SE) for the Hellmann potential which represents the superposition of the attractive Coulomb potential (-a/r) and the Yukawa potential bexp(-δ/r)/r of arbitrary strength b and screening parameter d in closed form. The analytical expressions to the energy eigenvalues Enl 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 d 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.