## Approximate Relativistic Solutions for a New Ring-Shaped Hulthén Potential

Journal Title, Volume, Page:
Z. Naturforsch. 68a (3-4) (2013) 279-290
Year of Publication:
2013
Authors:
Sameer M. Ikhdair
Physics Department, Faculty of Science, An-Najah National University, Nablus, Palestine
Current Affiliation:
Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine
Majid Hamzavi
Department of Science and Engineering, Abhar Branch, Islamic Azad University, Abhar, Iran
Preferred Abstract (Original):

Approximate bound state solutions of the Dirac equation with the Hulth\'en plus a new generalized ring-shaped (RS) potential are obtained for any arbitrary -state. The energy eigenvalue equation and the corresponding two-component wave function are calculated by solving the radial and angular wave equations within a recently introduced shortcut of Nikiforov-Uvarov (NU) method. The solutions of the radial and polar angular parts of the wave function are given in terms of the Jacobi polynomials. We use an exponential approximation in terms of the Hulthen potential parameters to deal with the strong singular centrifugal potential term Under the limiting case, the solution can be easily reduced to the solution of the Schrodinger equation with a new ring-shaped Hulth\'en potential.

## Relativistic Symmetries in the Rosen Morse Potential and Tensor Interaction using the Nikiforov Uvarov Method

Journal Title, Volume, Page:
Chin. Phys. B Vol. 22, No. 4 (2013) 040302
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
Majid Hamzavi
Department of Science and Engineering, Abhar Branch, Islamic Azad University, Abhar, Iran
Preferred Abstract (Original):

Approximate analytical bound-state solutions of the Dirac particle in the field of both attractive and repulsive RM potentials including Coulomb-like tensor (CLT) potential are obtained for arbitrary spin-orbit quantum number The Pekeris approximation is used to deal with the spin-orbit coupling terms In the presence of exact spin and pseudospin (p-spin) symmetries, the energy eigenvalues and the corresponding normalized two-component wave functions are found by using the parametric generalization of the Nikiforov-Uvarov (NU) method. The numerical results show that the CLT interaction removes degeneracies between spin and p-spin state doublets.

## Effective Schrödinger Equation with General Ordering Ambiguity Position-Dependent Mass Morse Potential

Journal Title, Volume, Page:
Molecular Physics: An International Journal at the Interface Between Chemistry and Physics Volume 110, Issue 13, 1415-1428
Year of Publication:
2012
Authors:
Sameer M. Ikhdair
Physics Department, Near East University, Nicosia, North Cyprus, Turkey
Current Affiliation:
Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine
Preferred Abstract (Original):
We solve the parametric generalized effective Schrödinger equation with a specific choice of position-dependent mass function and Morse oscillator potential by means of the Nikiforov–Uvarov method combined with the Pekeris approximation scheme. All bound-state energies are found explicitly and all corresponding radial wave functions are built analytically. We choose the Weyl or Li and Kuhn ordering for the ambiguity parameters in our numerical work to calculate the energy spectrum for a few (H2, LiH, HCl and CO) diatomic molecules with arbitrary vibration n and rotation l quantum numbers and different position-dependent mass functions. Two special cases including the constant mass and the vibration s-wave (l = 0) are also investigated.

## Exact Solutions of Feinberg-Horodecki Equation for Time-Dependent Deng-Fan Molecular Potential

Journal Title, Volume, Page:
Journal of Theoretical and Applied Physics 2013, 7:40
Year of Publication:
2013
Authors:
Sameer M Ikhdair
Department of Physics, Faculty of Science, An-Najah National University, Nablus, West Bank, Palestine
Current Affiliation:
Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine
Majid Hamzavi
Department of Physics, Faculty of Science, An-Najah National University, Nablus, West Bank, Palestine
Majid Amirfakhrian
Department of Physics, Faculty of Science, An-Najah National University, Nablus, West Bank, Palestine
Preferred Abstract (Original):

The exact bound state solutions of the Feinberg-Horodecki equation with the rotating time-dependent Deng-Fan oscillator potential are presented within the framework of the generalized parametric Nikiforov-Uvarov method. It is shown that the solutions can be expressed in terms of Jacobi polynomials or the generalized hypergeometric functions. The energy eigenvalues and the corresponding wave functions are obtained in closed forms.

## A Charged Spinless Particle in Scalar–Vector Harmonic Oscillators with Uniform Magnetic and Aharonov–Bohm Flux Fields

Journal Title, Volume, Page:
Journal of the Association of Arab Universities for Basic and Applied Sciences
Year of Publication:
2013
Authors:
Sameer M. Ikhdair
Department of Physics, Faculty of Science, An-Najah National University, New Campus, Jenaid, Nablus, West Bank, Palestine
Current Affiliation:
Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine
Babatunde J. Falaye
Theoretical Physics Section, Physics Department, University of Ilorin, P.M.B. 1515 Ilorin, Nigeria
Preferred Abstract (Original):

The two-dimensional solution of the spinless Klein–Gordon (KG) equation for scalar–vector harmonic oscillator potentials with and without the presence of constant perpendicular magnetic and Aharonov–Bohm (AB) flux fields is studied within the asymptotic function analysis and Nikiforov–Uvarov (NU) method. The exact energy eigenvalues and normalized wave functions are analytically obtained in terms of potential parameters, magnetic field strength, AB flux field and magnetic quantum number. The results obtained by using different Larmor frequencies are compared with the results in the absence of both magnetic field (ωL = 0) and AB flux field (ξ = 0) case. Effects of external fields on the non-relativistic energy eigenvalues and wave functions solutions are also precisely presented.

## Exact Polynomial Solution of PT -/Non-PT - Symmetric and Non-Hermitian Modiﬁed Woods– Saxon Potential by the Nikiforov–Uvarov Method

Journal Title, Volume, Page:
International Journal of Theoretical Physics, Volume 46, Issue 6, pp 1643-1665
Year of Publication:
2007
Authors:
Sameer M. Ikhdair
Department of Physics, Near East University, Nicosia, Mersin 10, North Cyprus, Turkey
Current Affiliation:
Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine
Ramazan Sever
Department of Physics, Middle East Technical University, 06531, Ankara, Turkey
Preferred Abstract (Original):
Using the Nikiforov–Uvarov (NU) method, the bound state energy eigenvalues and eigenfunctions of the
PT$−/non−$PT
-symmetric and non-Hermitian modified Woods–Saxon (WS) model potential with the real and complex-valued energy levels are obtained in terms of the Jacobi polynomials. According to the PT -symmetric quantum mechanics, we exactly solved the time-independent Schrödinger equation with same potential for the s-states and also for any l-state as well. It is shown that the results are in good agreement with the ones obtained before.

## Bound-States of A Semi-Relativistic Equation for the PT- Symmetric Generalized Hulthén Potential by the Nikiforov–Uvarov Method

Journal Title, Volume, Page:
International Journal of Modern Physics E Vol. 17, No. 6, 1107- 1123
Year of Publication:
2008
Authors:
SAMEER M. IKHDAIR
Department of Physics, Near East University, Nicosia, TRNC, Mersin 10, Turkey
Current Affiliation:
Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine
RAMAZAN SEVER
Department of Physics, Middle East Technical University, 06531 Ankara, Turkey
Preferred Abstract (Original):

The one-dimensional semi-relativistic equation has been solved for the -symmetric generalized Hulthén potential. The Nikiforov–Uvarov (NU) method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type, is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have investigated the positive and negative exact bound states of the s-states for different types of complex generalized Hulthén potentials.

## Spin And Pseudospin Symmetries In Relativistic Trigonometric Pöschl Teller Potential With Centrifugal Barrier

Journal Title, Volume, Page:
International Journal of Modern Physics E Vol. 21, No. 12
Year of Publication:
2012
Authors:
S. M. IKHDAIR
Physics Department, Near East University, 922022 Nicosia, North Cyprus, Mersin 10, Turkey
Current Affiliation:
Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine
K.-E. THYLWE
KTH-Mechanics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
M. HAMZAVI
Department of Basic Sciences, Shahrood Branch, Islamic Azad University, Shahrood, Iran
Preferred Abstract (Original):

Approximate analytical solutions of the Dirac equation with the trigonometric Pöschl–Teller (tPT) potential are obtained for arbitrary spin-orbit quantum number κ using an approximation scheme to deal with the spin-orbit coupling terms κ(κ±1)r-2. In the presence of exact spin and pseudo-spin (p-spin) symmetric limitation, the bound state energy eigenvalues and the corresponding two-component wave functions of the Dirac particle moving in the field of attractive and repulsive tPT potential are obtained using the parametric generalization of the Nikiforov–Uvarov (NU) method. The case of nonrelativistic limit is studied too.

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

Journal Title, Volume, Page:
Chin. Phys. B Vol. 22, No. 4, 040302
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
Babatunde J. Falaye
Department of Science and Engineering, Abhar Branch, Islamic Azad University, Abhar, Iran
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.

## Exact Solutions of Feinberg-Horodecki Equation for Time-Dependent Deng-Fan Molecular Potential

Journal Title, Volume, Page:
Journal of Theoretical and Applied Physics, 7, 40
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, An-Najah National University, Nablus, Palestine
Majid Hamzavi
Department of Science and Engineering, Abhar Branch, Islamic Azad University, Abhar, Iran
Majid Amirfakhrian
Department of Science and Engineering, Abhar Branch, Islamic Azad University, Abhar, Iran
Preferred Abstract (Original):

The exact bound state solutions of the Feinberg-Horodecki equation with the rotating time-dependent Deng-Fan oscillator potential are presented within the framework of the generalized parametric Nikiforov-Uvarov method. It is shown that the solutions can be expressed in terms of Jacobi polynomials or the generalized hypergeometric functions. The energy eigenvalues and the corresponding wave functions are obtained in closed forms.