Approximation Schemes | An-Najah Staff

Approximate Relativistic Solutions for a New Ring-Shaped Hulthén Potential

Wed, 2013-10-30 09:29 — Sameer. Ikhdair

Journal Title, Volume, Page:

Z. Naturforsch. 68a (3-4) (2013) 279-290

Year of Publication:

2013

Link:

http://arxiv.org/abs/1307.8306

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

[email protected]

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

Wed, 2013-10-30 09:18 — Sameer. Ikhdair

Journal Title, Volume, Page:

Chin. Phys. B Vol. 22, No. 4 (2013) 040302

Year of Publication:

2013

Link:

http://arxiv.org/abs/1307.8311

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]

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.

Equivalence of the Empirical Shifted Deng–Fan Oscillator Potential for Diatomic Molecules

Tue, 2013-10-29 12:30 — Sameer. Ikhdair

Journal Title, Volume, Page:

Journal of Mathematical Chemistry, Volume 51, Issue 1, pp 227-238

Year of Publication:

2013

Link:

http://link.springer.com/article/10.1007%2Fs10910-012-0075-x

Authors:

S. M. Ikhdai

Physics Department, Near East University, North Cyprus, Mersin 10, 922022, Nicosia, Turkey

Current Affiliation:

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

[email protected]

M. Hamzavi

Department of Basic Sciences, Shahrood Branch, Islamic Azad University, Shahrood, Iran

K.-E. Thylwe

KTH-Mechanics, Royal Institute of Technology, 100 44, Stockholm, Sweden

Preferred Abstract (Original):

We obtain the bound-state solutions of the radial Schrödinger equation with the shifted Deng–Fan oscillator potential in the frame of the Nikiforov-Uvarov method by employing Pekeris-type approximation to deal with the centrifugal term. The analytical expressions for the energy eigenvalues and the corresponding normalized wave functions are obtained in closed form for arbitrary l-state. The ro-vibrational energy levels for a few diatomic molecules are also calculated. They are found to be in good agreement with those ones previously obtained by the Morse potential.

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

Tue, 2013-10-29 09:00 — Sameer. Ikhdair

Journal Title, Volume, Page:

International Journal of Modern Physics E Vol. 21, No. 12

Year of Publication:

2012

Link:

http://www.worldscientific.com/doi/abs/10.1142/S0218301312500978

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

[email protected]

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

Mon, 2013-09-16 10:57 — Sameer. Ikhdair

Journal Title, Volume, Page:

Chin. Phys. B Vol. 22, No. 4, 040302

Year of Publication:

2013

Link:

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

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

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.

Approximate Bound States of the Dirac Equation with Some Physical Quantum Potentials

Sun, 2013-09-15 08:18 — Sameer. Ikhdair

Journal Title, Volume, Page:

Volume 218, Issue 20 , Pages 10082–10093

Year of Publication:

2012

Link:

http://www.sciencedirect.com/science/article/pii/S0096300312003311

Authors:

Sameer M. Ikhdair

Physics Department, Near East University, 922022 Nicosia, North Cyprus, Turkey

Current Affiliation:

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

[email protected]

Ramazan Sever

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

Preferred Abstract (Original):

The approximate analytical solutions of the Dirac equations with the reflectionless-type and Rosen–Morse potentials including the spin–orbit centrifugal (pseudo-centrifugal) term are obtained. Under the conditions of spin and pseudospin (pspin) symmetry concept, we obtain the bound state energy spectra and the corresponding two-component upper- and lower-spinors of the two Dirac particles by means of the Nikiforov–Uvarov (NU) method in closed form. The special cases of the s-wave Dirac equation and the non-relativistic limit of Dirac equation are briefly studied.

Klein–Gordon Solutions for a Yukawa-like Potential

Sun, 2013-09-15 08:12 — Sameer. Ikhdair

Journal Title, Volume, Page:

Z. Naturforsch. XXX, 1 – 10

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]

Preferred Abstract (Original):

The Klein–Gordon equation for a recently proposed Yukawa-type potential is solved with any or-bital quantum number l. In the equally mixed scalar-vector potential ﬁelds $S(r) = \pm V(r)$ the approximateenergy eigenvalues and their wave functions for a particle and anti-particle are obtained by means of the parametric Nikiforov–Uvarov method. The non-relativistic solutions are also investigated. It is found that the present analytical results are in exact agreement with the previous ones.

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.

Two Approximation Schemes to The Bound States of the Dirac–Hulthén Problem

Thu, 2013-09-12 11:06 — Sameer. Ikhdair

Journal Title, Volume, Page:

Journal of Physics A Mathematical and Theoretical, 44(35):355301

Year of Publication:

2011

Link:

http://www.researchgate.net/publication/231134164_Two_approximation_schemes_to_t...

Authors:

Sameer M Ikhdair

Physics Department, Near East University, Nicosia, North Cyprus, Turkey

Current Affiliation:

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

[email protected]

Ramazan Sever

Physics Department, Middle East Technical University, 06800, Ankara, Turkey

Preferred Abstract (Original):

The bound-state (energy spectrum and two-spinor wavefunctions) solutions of the Dirac equation with the Hulthén potential for all angular momenta based on the spin and pseudospin symmetry are obtained. The parametric generalization of the Nikiforov–Uvarov method is used in the calculations. The orbital dependence (spin–orbit- and pseudospin–orbit-dependent coupling too singular 1/r2) of the Dirac equation are included to the solution by introducing a more accurate approximation scheme to deal with the centrifugal (pseudo-centrifugal) term. The approximation is also made for the less singular 1/r orbital term in the Dirac equation for a wider energy spectrum. The nonrelativistic limits are also obtained on mapping of parameters.

Bound States of the Klein-Gordon for Exponential-Type Potentials in D-Dimensions

Wed, 2013-09-11 08:29 — Sameer. Ikhdair

Journal Title, Volume, Page:

Journal of Quantum Information Science, 1, 73-86

Year of Publication:

2011

Link:

http://www.scirp.org/journal/PaperInformation.aspx?paperID=7631

Authors:

Sameer M. Ikhdair

Physics Department, Near East University, Nicosia, North Cyprus, Turkey

Current Affiliation:

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

[email protected]

Preferred Abstract (Original):

The approximate analytic bound state solutions of the Klein-Gordon equation with equal scalar and vector exponential-type potentials including the centrifugal potential term are obtained for any arbitrary orbital quantum number l and dimensional space D. The relativistic/non-relativistic energy spectrum formula and the corresponding un-normalized radial wave functions, expressed in terms of the Jacobi polynomials and or the generalized hypergeometric functions have been obtained. A short-cut of the Nikiforov-Uvarov (NU) method is used in the solution. A unified treatment of the Eckart, Rosen-Morse, Hulthén and Woods-Saxon potential models can be easily derived from our general solution. The present calculations are found to be identical with those ones appearing in the literature. Further, based on the PT-symmetry, the bound state solutions of the trigonometric Rosen-Morse potential can be easily obtained.