Hellmann Potential | An-Najah Staff

Approximate Eigensolutions of Dirac Equation for the Superposition Hellmann Potential Under Spin and ‎Pseudospin Symmetries

Tue, 2015-02-17 11:30 — Sameer. Ikhdair

Journal Title, Volume, Page:

Pramana , Volume 83, Issue 1, pp 49-61

Year of Publication:

2014

Link:

http://link.springer.com/article/10.1007%2Fs12043-014-0764-z

Authors:

S M IKHDAIR

Department of Physics, Faculty of Science, An- Najah National University, New Campus, Nablus, Palestine

Current Affiliation:

Department of Physics, Faculty of Science, An-Najah National University, New campus, P. O. Box 7, Nablus, Palestine

[email protected]

M HAMZAVI

Department of Science and Engineering, Abhar Branch, Islamic Azad University, Abhar, Iran

Preferred Abstract (Original):

The Hellmann potential is simply a superposition of an attractive Coulomb potential −a/r plus a Yukawa potential be−δ r /r. The generalized parametric Nikiforov–Uvarov (NU) method is used to examine the approximate analytical energy eigenvalues and two-component wave function of the Dirac equation with the Hellmann potential for arbitrary spin-orbit quantum number κ in the presence of exact spin and pseudospin (p-spin) symmetries. As a particular case, we obtain the energy eigenvalues of the pure Coulomb potential in the non-relativistic limit.

A Perturbative Treatment for the Bound States of the Hellmann Potential

Wed, 2013-10-30 12:43 — Sameer. Ikhdair

Journal Title, Volume, Page:

Journal of Molecular Structure: THEOCHEM 809, 103–113

Year of Publication:

2007

Link:

http://arxiv.org/abs/quant-ph/0603205

Authors:

Sameer M Ikhdair

Department of Physics, Near East University, Nicosia, North Cyprus, Mersin-10, Turkey

Current Affiliation:

Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine

[email protected]

Ramazan Sever

Department of Physics, Middle East Technical University, 06531 Ankara, Turkey

Preferred Abstract (Original):

A new approximation formalism is applied to study the bound states of the Hellmann potential, which represents the superposition of the attractive Coulomb potential −a/r and the Yukawa potential bexp(−δr)/r of arbitrary strength b and screening parameter δ. Although the analytic expressions for the energy eigenvalues En,l yield quite accurate results for a wide range of n,ℓ in the limit of very weak screening, the results become gradually worse as the strength b and the screening coefficient δ increase. This is because that the expansion parameter is not sufficiently small enough to guarantee the convergence of the expansion series for the energy levels.

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

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.