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

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Sun, 2013-09-15 07:59 — Sameer. Ikhdair
Journal Title, Volume, Page: 
Z. Naturforsch. XXX, 1 – 8
Year of Publication: 
2013
Authors: 
Sameer M. Ikhdair
Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine
Current Affiliation: 
Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine
[email protected]
Babatunde J. Falaye
Theoretical Physics Section, Department of Physics, University of Ilorin, P. M. B. 1515, Ilorin, Nigeria
Preferred Abstract (Original): 

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 bexp(-\delta \!\,r) /r of arbitrary strength b and screening parameter \delta \!\,in closed form. The analytical expressions to the energy eigenvalues E 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.