scholarly journals SOLUTIONS OF THE DIRAC EQUATION WITH THE SHIFTED DENG–FAN POTENTIAL INCLUDING YUKAWA-LIKE TENSOR INTERACTION

2013 ◽  
Vol 22 (08) ◽  
pp. 1350062 ◽  
Author(s):  
W. A. YAHYA ◽  
B. J. FALAYE ◽  
O. J. OLUWADARE ◽  
K. J. OYEWUMI
Keyword(s):  
Dirac Equation ◽  
Analytical Solutions ◽  
Approximation Scheme ◽  
Pseudospin Symmetry ◽  
Tensor Interaction ◽  
Numerical Results ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions ◽  
Uvarov Method

By using the Nikiforov–Uvarov method, we give the approximate analytical solutions of the Dirac equation with the shifted Deng–Fan potential including the Yukawa-like tensor interaction under the spin and pseudospin symmetry conditions. After using an improved approximation scheme, we solved the resulting schrödinger-like equation analytically. Numerical results of the energy eigenvalues are also obtained, as expected, the tensor interaction removes degeneracies between spin and pseudospin doublets.

APPROXIMATE RELATIVISTIC κ-STATE SOLUTIONS TO THE DIRAC-HYPERBOLIC PROBLEM WITH GENERALIZED TENSOR INTERACTIONS

2013 ◽  
Vol 22 (07) ◽  
pp. 1350048 ◽  
Author(s):  
AKPAN N. IKOT ◽  
H. HASSANABADI ◽  
B. H. YAZARLOO ◽  
S. ZARRINKAMAR
Keyword(s):  
Dirac Equation ◽  
Analytical Solutions ◽  
Tensor Interaction ◽  
Numerical Results ◽  
Hyperbolic Problem ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions ◽  
Frame Work ◽  
Nu Method

In this paper, we present the approximate analytical solutions of the Dirac equation for hyperbolical potential within the frame work of spin and pseudospin symmetries limit including the newly proposed generalized tensor interaction (GTI) using the Nikiforov–Uvarov (NU) technique. We obtained the energy eigenvalues and the corresponding eigenfunction using the generalized parametric NU method. The numerical results of our work reveal that the presence of the GTI changes the degeneracy between the spin and pseudospin state doublets.

Solutions of the Dirac equation with an improved expression of the Rosen–Morse potential energy model including Coulomb-like tensor interaction

2013 ◽  
Vol 91 (9) ◽  
pp. 689-695 ◽  
Author(s):  
Ekele V. Aguda
Keyword(s):  
Dirac Equation ◽  
Potential Energy ◽  
Analytical Solutions ◽  
Morse Potential ◽  
Analytical Approach ◽  
Pseudospin Symmetry ◽  
Tensor Interaction ◽  
Energy Model ◽  
Approximate Analytical Solutions ◽  
Uvarov Method

In this study, we obtain the approximate analytical solutions of the Dirac equation for an improved expression of the Rosen–Morse potential energy model including the Coulomb-like tensor under the condition of spin and pseudospin symmetry. The analytical approach of parametric generalization of the Nikiforov–Uvarov method has been applied to the problem and the problem is discussed in a quite detailed manner.

scholarly journals Pseudospin and Spin Symmetric Solutions of the Dirac Equation: Hellmann Potential,Wei–Hua Potential, Varshni Potential

2014 ◽  
Vol 69 (3-4) ◽  
pp. 163-172 ◽  
Author(s):  
Altuğ Arda ◽  
Ramazan Sever
Keyword(s):  
Dirac Equation ◽  
Analytical Solutions ◽  
Energy Eigenvalue ◽  
Wave Functions ◽  
K Value ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions ◽  
Hellmann Potential ◽  
Uvarov Method ◽  
Spinor Wave

Approximate analytical solutions of the Dirac equation are obtained for the Hellmann potential, the Wei-Hua potential, and the Varshni potential with any k-value for the cases having the Dirac equation pseudospin and spin symmetries. Closed forms of the energy eigenvalue equations and the spinor wave functions are obtained by using the Nikiforov-Uvarov method and some tables are given to see the dependence of the energy eigenvalues on different quantum number pairs (n;κ).

EXACTLY COMPLETE SOLUTIONS OF THE DIRAC EQUATION WITH PSEUDOHARMONIC POTENTIAL INCLUDING LINEAR PLUS COULOMB-LIKE TENSOR POTENTIAL

2011 ◽  
Vol 26 (07n08) ◽  
pp. 1363-1374 ◽  
Author(s):  
M. HAMZAVI ◽  
A. A. RAJABI ◽  
H. HASSANABADI
Keyword(s):  
Dirac Equation ◽  
Pseudospin Symmetry ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Spin Orbit Coupling ◽  
Energy Eigenvalues ◽  
Pseudoharmonic Potential ◽  
Tensor Potential ◽  
Uvarov Method ◽  
Coupling Number

In this paper, we present exact solutions of the Dirac equation with the pseudoharmonic potential including linear as well as Coulomb-like tensor potential with arbitrary spin–orbit coupling number κ under spin and pseudospin symmetry limits. The Nikiforov–Uvarov method is used to obtain energy eigenvalues and corresponding eigenfunctions in closed forms. We show that tensor interaction removes degeneracies between spin and pseudospin doublets. Some numerical results are also given.

Dirac equation with multiparameter-potential and Hulthén tensor interaction under relativistic symmetries

Open Physics ◽  
2014 ◽  
Vol 12 (12) ◽  
Author(s):  
Sami Ortakaya
Keyword(s):  
Dirac Equation ◽  
Spin Symmetry ◽  
Tensor Interaction ◽  
Numerical Results ◽  
Exponential Potential ◽  
Energy Eigenvalues ◽  
Nu Method

AbstractThe pseudospin and spin symmetric solutions of the Dirac equation with Hulthén-type tensor interaction are obtained under multi-parameter-exponential potential (MEP) for arbitrary κ states. The energy eigenvalues and the corresponding eigenfunctions are also obtained using the parametric Nikiforov-Uvarov (NU) method. Some numerical results are also obtained for pseudospin and spin symmetry limits.

scholarly journals Eigen Spectra for q-Deformed Hyperbolic Scarf Potential Including a Coulomb-like Tensor Interaction

2011 ◽  
Vol 3 (2) ◽  
pp. 239-247 ◽  
Author(s):  
M. Eshghi ◽  
H. Mehraban
Keyword(s):  
Dirac Equation ◽  
Spin Symmetry ◽  
Tensor Interaction ◽  
Tensor Coupling ◽  
Energy Eigenvalues ◽  
Scarf Potential ◽  
Tensor Potential ◽  
Uvarov Method

We study the Dirac equation for the q-deformed hyperbolic Scarf potential including a coulomb-like tensor potential under the spin symmetry. The parametric generalization of the Nikiforov-Uvarov method is used to obtain the energy eigenvalues equation and the unnormalized wave functins.Keywords: Dirac equation; q-deformed hyperbolic Scarf; Spin symmetry; Tensor coupling.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i2.7295                 J. Sci. Res. 3 (2), 239-247 (2011)

scholarly journals Pseudo-spin Symmetry for Relativistic-Hyperbolic Problem and Tensor Potential

2011 ◽  
Vol 3 (3) ◽  
pp. 493-500 ◽  
Author(s):  
M. Eshghi
Keyword(s):  
Dirac Equation ◽  
Relativistic Equation ◽  
Spin Symmetry ◽  
Numerical Results ◽  
Wave Functions ◽  
Hyperbolic Problem ◽  
Energy Eigenvalues ◽  
Tensor Potential ◽  
Hyperbolic Potential ◽  
Uvarov Method

We study the relativistic equation of spin-1/2 particles under the hyperbolic potential and a Coulomb-like tensor potential. By using the generalized parametric of the Nikiforov-Uvarov method and the pseudo-spin symmetry, we obtain the energy eigenvalues equation and the corresponding unnormalized wave functions. Some numerical results are given, too.Keywords: Dirac equation; Tensor potential; Pseudo-spin symmetry; Nikiforov-Uvarov.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserveddoi:10.3329/jsr.v3i3.8071               J. Sci. Res. 3 (3), 503-510 (2011

scholarly journals The Effect of Tensor Interaction in Splitting the Energy Levels of Relativistic Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Mohammad Reza Shojaei ◽  
Mohsen Mousavi
Keyword(s):  
Dirac Equation ◽  
Present Model ◽  
Energy Levels ◽  
Pseudospin Symmetry ◽  
Spin Symmetry ◽  
Tensor Interaction ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Formula Method ◽  
Dirac Spinors

We solve approximately Dirac equation for Eckart plus Hulthen potentials with Coulomb-like and Yukawa-like tensor interaction in the presence of spin and pseudospin symmetry fork≠0. The formula method is used to obtain the energy eigenvalues and wave functions. We also discuss the energy eigenvalues and the Dirac spinors for Eckart plus Hulthen potentials with formula method. To show the accuracy of the present model, some numerical results are shown in both pseudospin and spin symmetry limits.

scholarly journals Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

Open Physics ◽  
2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Sameer Ikhdair ◽  
Ramazan Sever
Keyword(s):  
Analytical Solutions ◽  
Pseudospin Symmetry ◽  
Spin Symmetry ◽  
Bound State ◽  
S Wave ◽  
Relativistic Limit ◽  
Approximate Analytical Solutions ◽  
Special Cases ◽  
Linear Differential ◽  
Uvarov Method

AbstractWe study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. We apply the Nikiforov-Uvarov method (which solves a second-order linear differential equation by reducing it to a generalized hypergeometric form) to spin- and pseudospin-symmetry to obtain, in closed form, the approximately analytical bound state energy eigenvalues and the corresponding upper- and lower-spinor components of two Dirac particles. The special cases κ = ±1 (s = $$ \tilde l $$ = 0, s-wave) and the non-relativistic limit can be reached easily and directly for the generalized and standard Woods-Saxon potentials. We compare the non-relativistic results with those obtained by others.

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