scholarly journals Spin and Pseudospin Symmetry in Generalized Manning-Rosen Potential

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Hilmi Yanar ◽  
Ali Havare
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Pseudospin Symmetry ◽  
Molecular Structures ◽  
Centrifugal Term ◽  
Term Energy ◽  
Energy Relations ◽  
Rosen Potential ◽  
Uvarov Method ◽  
Pekeris Approximation

Spin and pseudospin symmetric Dirac spinors and energy relations are obtained by solving the Dirac equation with centrifugal term for a new suggested generalized Manning-Rosen potential which includes the potentials describing the nuclear and molecular structures. To solve the Dirac equation the Nikiforov-Uvarov method is used and also applied the Pekeris approximation to the centrifugal term. Energy eigenvalues for bound states are found numerically in the case of spin and pseudospin symmetry. Besides, the data attained in the present study are compared with the results obtained in the previous studies and it is seen that our data are consistent with the earlier ones.

Spin-one Duffin–Kemmer–Petiau equation in the presence of Manning–Rosen potential plus a ring-shaped-like potential

2014 ◽  
Vol 92 (6) ◽  
pp. 465-471 ◽  
Author(s):  
H. Hassanabadi ◽  
M. Kamali ◽  
B.H. Yazarloo
Keyword(s):  
Jacobi Polynomials ◽  
Dimensional Space ◽  
Space Time ◽  
Numerical Results ◽  
Centrifugal Term ◽  
Exponential Approximation ◽  
3 Dimensional ◽  
Dimensional Space Time ◽  
Rosen Potential ◽  
Uvarov Method

We present the solution of the Duffin–Kemmer–Petiau equation for Manning–Rosen potential plus a ring-shaped-like potential in (1+3)-dimensional space–time for spin-one particles within the framework of an exponential approximation for the centrifugal term. We have used the Nikiforov–Uvarov method in our calculations. The radial wavefunction and the angular wavefunctions are expressed in terms of Jacobi polynomials. We have also represented some numerical results for the Manning–Rosen potential plus a ring-shaped-like potential.

Solution of the Dirac equation with exponential-type potential under the GUP

2021 ◽  
Vol 36 (01) ◽  
pp. 2150005
Author(s):  
Lin-Fang Deng ◽  
He-Yao Zhang ◽  
Chao-Yun Long
Keyword(s):  
Dirac Equation ◽  
Uncertainty Principle ◽  
Exponential Type ◽  
Generalized Uncertainty Principle ◽  
Pseudospin Symmetry ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty ◽  
Uvarov Method ◽  
Planck Energy ◽  
Type Potential

In quantum gravity theories, when the scattering energy is comparable to the Planck energy, the usual Heisenberg uncertainty principle breaks down and is replaced by generalized uncertainty principle (GUP). In this paper, the Dirac equation is studied for a single particle with spin and pseudospin symmetry in the presence of GUP, in [Formula: see text] dimensions. For arbitrary wave [Formula: see text], the Dirac equation with multiparameter exponential-type potential is solved by applying the approximation of the centrifugal term and the Nikiforov–Uvarov method. The corresponding energy spectra and eigenvalue function are obtained in the closed form and depend on the GUP parameter. In addition, several interesting cases have been discussed.

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.

GALILEAN COVARIANT DIRAC EQUATION WITH A WOODS–SAXON POTENTIAL

2013 ◽  
Vol 22 (12) ◽  
pp. 1350092 ◽  
Author(s):  
A. A. OTHMAN ◽  
M. DE MONTIGNY ◽  
F. C. KHANNA
Keyword(s):  
Dirac Equation ◽  
Dimensional Manifold ◽  
Saxon Potential ◽  
Eigenvalues And Eigenfunctions ◽  
Covariant Approach ◽  
Energy Eigenvalues ◽  
Energy Eigenvalues And Eigenfunctions ◽  
Galilean Space ◽  
Uvarov Method ◽  
Pekeris Approximation

We derive and solve the Galilean covariant Dirac equation, also called "Lévy-Leblond equation", for spin-½ particles in a Woods–Saxon potential. We obtain this wave equation with a Galilean covariant approach, which is based on a (4+1)-dimensional manifold with light-cone coordinates followed by a reduction to the (3+1)-dimensional Galilean space-time. We apply the Pekeris approximation and exploit the Nikiforov–Uvarov method to find the energy eigenvalues and eigenfunctions.

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 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.

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