asymptotic iteration method

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.

Relativistic Symmetries with the Trigonometric Pöschl Teller Potential Plus Coulomb-Like Tensor Interaction

Thu, 2013-09-12 12:58 — Sameer. Ikhdair

Journal Title, Volume, Page:

Chin. Phys. B Vol. 22, No. 6 060305

Year of Publication:

2013

Link:

http://iopscience.iop.org/1674-1056/22/6/060305

Authors:

Sameer M. Ikhdair

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

Current Affiliation:

Department of Physics, 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 Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Pöschl—Teller (tPT) potential including a Coulomb-like tensor interaction with arbitrary spin—orbit quantum number κ using an approximation scheme to substitute the centrifugal terms κ(κ ± 1)r⁻². In view of spin and pseudo-spin (p-spin) symmetries, the relativistic energy eigenvalues and the corresponding two-component wave functions of a particle moving in the field of attractive and repulsive tPT potentials are obtained using the asymptotic iteration method (AIM). We present numerical results in the absence and presence of tensor coupling A and for various values of spin and p-spin constants and quantum numbers n and κ. The non-relativistic limit is also obtained.

An-Najah Staff