Approximate Bound States Solution of the Hellmann Potential

Abstract

The Hellmann potential, which is a superposition of an attractive Coulomb potential −a/r and a Yukawa potential b e−δr/r, is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov—Uvarov (NU) method, we have obtained the approximate analytical solutions of the radial Schrödinger equation (SE) for the Hellmann potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented, which show good agreement with a numerical amplitude phase method and also those previously obtained by other methods. As a particular case, we find the energy levels of the pure Coulomb potential.