## Approximate Eigenvalue and Eigenfunction Solutions for the Generalized Hulthén Potential with any Angular Momentum

Journal Title, Volume, Page:
Journal of Mathematical Chemistry, Vol. 42, No. 3
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):

An approximate solution of the Schrödinger equation for the generalized Hulthén potential with non-zero angular quantum number is solved. The bound state energy eigenvalues and eigenfunctions are obtained in terms of Jacobi polynomials. The Nikiforov–Uvarov method is used in the computations. We have considered the time-independent Schrödinger equation with the associated form of Hulthén potential which simulate the effect of the centrifugal barrier for any l-state. The energy levels of the used Hulthén potential gives satisfactory values for the non-zero angular momentum as the generalized Hulthén effective potential.

## Polynomial Solution of Non-Central Potentials

Journal Title, Volume, Page:
Int J Theor Phys , 46: 2384–2395
Year of Publication:
2007
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
Ramazan Sever
Department of Physics, Middle East Technical University, 06531 Ankara, Turkey
Preferred Abstract (Original):
We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov-Bohm potentials as special cases. The results are in exact agreement with other methods.

## 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.

## Exact Bound States of the D-Dimensional Klein Gordon Equation with Equal Scalar and Vector Ring-Shaped Pseudoharmonic Potential

Journal Title, Volume, Page:
International Journal of Modern Physics C Vol. 19, No. 9, 1425-1442
Year of Publication:
2008
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
Ramazan Sever
Department of Physics, Middle East Technical University, 06531 Ankara, Turkey
Preferred Abstract (Original):

We present the exact solution of the Klein–Gordon equation in D-dimensions in the presence of the equal scalar and vector pseudoharmonic potential plus the ring-shaped potential using the Nikiforov–Uvarov method. We obtain the exact bound state energy levels and the corresponding eigen functions for a spin-zero particles. We also find that the solution for this ring-shaped pseudoharmonic potential can be reduced to the three-dimensional (3D) pseudoharmonic solution once the coupling constant of the angular part of the potential becomes zero.

## Exact Solutions of the Modified Kratzer Potential Plus Ring-Shaped Potential in the D-Dimensional Schrödinger Equation by the Nikiforov Uvarov Method

Journal Title, Volume, Page:
International Journal of Modern Physics C Vol. 19, No. 2, 221{235
Year of Publication:
2008
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
Ramazan Sever
Department of Physics Middle East Technical University 06531 Ankara, Turkey
Preferred Abstract (Original):
We present analytically the exact energy bound-states solutions of the Schrodinger equation in D-dimensions for a recently proposed modified Kratzer potential plus ring-shaped potential by means of the conventional Nikiforov-Uvarov method. We give a clear recipe of how to obtain an explicit solution to the wave functions in terms of orthogonal polynomials. The results obtained in this work are more general and true for any dimension which can be reduced to the standard forms in three-dimensions given by other works.

## Exact Solutions of the D-dimensional Schrödinger Equation for a Ring–shaped Pseudoharmonic Potential

Journal Title, Volume, Page:
Central European Journal of Physics September, Volume 6, Issue 3, pp 685-696
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):

A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form . The energy eigenvalues and eigenfunctions of the bound-states for the Schrödinger equation in D-dimensions for this potential are obtained analytically by using the Nikiforov-Uvarov method. The radial and angular parts of the wave functions are obtained in terms of orthogonal Laguerre and Jacobi polynomials. We also find that the energy of the particle and the wave functions reduce to the energy and the wave functions of the bound-states in three dimensions.

## Relativistic Solution in D-Dimensions to a Spin-Zero Particle for Equal Scalar and Vector Ring-Shaped Kratzer Potential

Journal Title, Volume, Page:
Cent. Eur. J. Phys., 6(1), 141-152
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 Klein-Gordon equation in D-dimensions for a recently proposed ring-shaped Kratzer potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound states and the corresponding wave functions of the Klein-Gordon are obtained in the presence of the non-central equal scalar and vector potentials. The results obtained in this work are more general and can be reduced to the standard forms in three dimensions given by other works.

## Exact Solution of the Klein-Gordon Equation for the PT-Symmetric Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method

Journal Title, Volume, Page:
Ann. Phys. (Leipzig) 16, No. 3, 218 – 232
Year of Publication:
2007
Authors:
Sameer M. Ikhdair
Department of Physics, Near East University, Nicosia, North Cyprus, Mersin 10, Turkey
Current Affiliation:
Physics Department, 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 Klein-Gordon (KG) equation has been solved for the PT-symmetric generalized Woods-Saxon (WS) 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 also investigated the positive and negative exact bound states of the s-states for different types of complex generalized WS potentials.