Z. Naturforsch. **68a,** 701 – 708
(2013)

doi:10.5560/ZNA.2013-0054

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

Sameer
M. Ikhdair^{1,2} and
Babatunde
J. Falaye^{3}

^{1 }Department of Physics, Near East University, 922022 Nicosia, Northern Cyprus, Turkey

^{2 }Department of Physics, Faculty of Science, an-Najah National University, Nablus, West Bank, Palestine

^{3 }Theoretical Physics Section, Department of Physics, University of Ilorin, P. M. B. 1515, Ilorin, Nigeria

Received January 30, 2013 / revised July 17, 2013 / published online September 18, 2013

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 Schrödinger equation (SE) for the Hellmann potential which represents the superposition of the attractive Coulomb potential (− *a*/*r*) and the Yukawa potential *b* exp (− *δr*)/*r* of arbitrary strength *b* and screening parameter *δ* 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 *δ* 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.

*Key words:* Schrödinger Equation; Hellmann Potential; Nikiforov–Uvarov Method; Asymptotic Iteration Method.

*PACS numbers:* 03.65.-w; 04.20.Jb; 03.65.Fd; 02.30.Gp; 03.65.Ge