Dirac equation

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Relativistic Effect of Pseudospin Symmetry and Tensor Coupling on the Mie-Type Potential via Laplace ‎Transformation Method

Journal Title, Volume, Page: 
Chin. Phys. B Vol. 23, No. 12
Year of Publication: 
2014
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, West Bank, Palestine
M. Eshghi
Young Researchers and Elite Club, Central Tehran Branch, Islamic Azad University, Tehran, Iran
Preferred Abstract (Original): 

A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S(r) and a vector V(r) Mie-type potential in the radial coordinates, as well as a tensor potential U(r) in the form of Coulomb potential. In the pseudospin (p-spin) symmetry setting Σ = Cps and Δ = V(r), an analytical solution for exact bound states of the corresponding Dirac equation is found. The eigenenergies and normalized wave functions are presented and particular cases are discussed with any arbitrary spin—orbit coupling number κ. Special attention is devoted to the case Σ = 0 for which p-spin symmetry is exact. The Laplace transform approach (LTA) is used in our calculations. Some numerical results are obtained and compared with those of other methods.

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Bound States of Spatially Dependent Mass Dirac Equation with the Eckart Potential Including Coulomb Tensor ‎Interaction

Journal Title, Volume, Page: 
The European Physical Journal Plus , 129:1
Year of Publication: 
2014
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
Theoretical Physics Section, University of Ilorin, Ilorin, Nigeria
Preferred Abstract (Original): 

We investigate the approximate solutions of the Dirac equation with the position-dependent mass particle in the Eckart potential field including the Coulomb tensor interaction by using the parametric Nikiforov-Uvarov method. Taking an appropriate approximation to deal with the centrifugal term, the Dirac energy states and the corresponding normalized two-spinor components of the wave function are obtained in closed form. Some special cases of our solution are investigated. Furthermore, we present the correct solutions obtained via the asymptotic iteration method which are in agreement with the parametric Nikiforov-Uvarov method results.

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Dirac Bound States of Anharmonic Oscillator in External Fields

Journal Title, Volume, Page: 
Annals of Physics Volume 341, Pages 153–163
Year of Publication: 
2014
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, New campus, Nablus, Palestine
Majid Hamzavi
Department of Physics, University of Zanjan, Zanjan, Iran
Babatunde J. Falaye
Theoretical Physics Section, Department of Physics, University of Ilorin, P. M. B. 1515, Ilorin, Nigeria
Preferred Abstract (Original): 

We explore the effect of the external magnetic and Aharonov–Bohm (AB) flux fields on the energy levels of Dirac particle subjects to mixed scalar and vector anharmonic oscillator field in the two-dimensional (2D) space. We calculate the exact energy eigenvalues and the corresponding un-normalized two-spinor-components wave functions in terms of the chemical potential parameter, magnetic field strength, AB flux field and magnetic quantum number by using the Nikiforov–Uvarov (NU) method.

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Approximate Solutions to a Spatially-Dependent Mass Dirac Equation for Modified Hylleraas Plus Eckart Potential with Yukawa Potential as a Tensor

Journal Title, Volume, Page: 
Indian Journal of Physics, Volume 88, Issue 7, pp 695-707
Year of Publication: 
2014
Authors: 
Sameer 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, Nablus, Palestine
Majid Hamzavi
Department of Physics, University of Zanjan, Zanjan, Iran
Preferred Abstract (Original): 

In presence of spin (pseudo-spin) symmetry, approximate bounded fermionic (anti-fermionic) states of the effective mass Dirac equation for modified Hylleraas plus Eckart potential within Yukawa tensor interaction have been studied by means of the parametric Nikiforov–Uvarov method. We have obtained the analytical relativistic energy eigenvalues and their corresponding normalized two-spinor components of the wave functions in closed form by making an appropriate approximation to centrifugal (pseudo-centrifugal) term for any spin–orbit quantum number κ. Some special cases for various potential models have been investigated in relativistic and nonrelativistic limit. Further, numerical results for energy eigenvalues have been obtained within the exact spin and pseudo-spin symmetries.

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

Journal Title, Volume, Page: 
Pramana , Volume 83, Issue 1, pp 49-61
Year of Publication: 
2014
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
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.

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Eigensolution Techniques, Their Applications and the Fisher's Information Entropy of Tietz-Wei ‎Diatomic Molecular Model

Journal Title, Volume, Page: 
Physica Scripta ; 89(11):115204
Year of Publication: 
2014
Authors: 
Sameer M. Ikhdair
Department of Physics, Faculty of Science, An-Najah National University, New campus, P. O. Box 7, Nablus, Palestine
M. Hamzavi
Department of Physics, University of Zanjan, Zanjan, Iran
B. J. Falaye
Applied Theoretical Physics Division, Department of Physics, Federal University Lafia, P M B 146, Lafia, Nasarawa State, Nigeria
K. J. Oyewumi
Theoretical Physics Section, Department of Physics, University of Ilorin, P M B 1515, Ilorin, Nigeria
Preferred Abstract (Original): 

In this study, approximate analytical solution of Schr\"odinger, Klein-Gordon and Dirac equations under the Tietz-Wei (TW) diatomic molecular potential are represented by using an approximation for the centrifugal term. We have applied three types of eigensolution techniques; the functional analysis approach (FAA), supersymmetry quantum mechanics (SUSYQM) and asymptotic iteration method (AIM) to solve Klein-Gordon Dirac and Schr\"odinger equations, respectively. The energy eigenvalues and the corresponding eigenfunctions for these three wave equations are obtained and some numerical results and figures are reported. It has been shown that these techniques yielded exactly same results. some expectation values of the TW diatomic molecular potential within the framework of the Hellmann-Feynman theorem (HFT) have been presented. The probability distributions which characterize the quantum-mechanical states of TW diatomic molecular potential are analysed by means of complementary information measures of a probability distribution called the Fishers information entropy. This distribution has been described in terms of Jacobi polynomials, whose characteristics are controlled by the quantum numbers.

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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.

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Pseudospin Symmetry in the Relativistic Killingbeck Potential: Quasi-Exact Solution

Journal Title, Volume, Page: 
Z. Naturforsch. 67a, 567-571
Year of Publication: 
2012
Authors: 
Sameer 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
Majid Hamzavi
Department of Basic Sciences, Shahrood Branch, Islamic Azad University, Shahrood, Iran
Karl-Erik Thylwe
KTH-Mechanics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Preferred Abstract (Original): 

The Killingbeck potential consisting of the harmonic oscillator-plus-Cornell potential, is of great interest in high energy physics. The solution of Dirac equation with the Killingbeck potential is studied in the presence of the pseudospin (p-spin) symmetry within the context of the quasi-exact solutions. Two special cases of the harmonic oscillator and Coulomb potential are also discussed.

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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.

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Exact Solution of Dirac Equation with Charged Harmonic Oscillator in Electric Field: Bound States

Journal Title, Volume, Page: 
Journal of Modern Physics, 3, 170-179
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): 

In some quantum chemical applications, the potential models are linear combination of single exactly solvable potentials. This is the case equivalent of the Stark effect for a charged harmonic oscillator (HO) in a uniform electric field of specific strength (HO in an external dipole field). We obtain the exact s-wave solutions of the Dirac equation for some potential models which are linear combination of single exactly solvable potentials (ESPs). In the framework of the spin and pseudospin symmetric concept, we calculate the analytic energy spectrum and the corresponding two-component upper- and lower-spinors of the two Dirac particles by the Nikiforov-Uvarov (NU) method, in a closed form. The nonrelativistic limit of the solution is also studied and compared with the other works.

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