Actual and general Manning–Rosen potentials under spin and pseudospin symmetries of the Dirac equation

2012 ◽  
Vol 90 (7) ◽  
pp. 633-646 ◽  
Author(s):  
H. Hassanabadi ◽  
E. Maghsoodi ◽  
S. Zarrinkamar ◽  
H. Rahimov
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Comparative Study ◽  
Analytical Solutions ◽  
Tensor Interaction ◽  
Centrifugal Term ◽  
Supersymmetry Quantum Mechanics

The so-called general and actual Manning–Rosen potentials have been investigated under spin and pseudospin symmetries of the Dirac equation in a comparative study. By approximating the centrifugal term, we have reported the analytical solutions to the problem via supersymmetry quantum mechanics. Illustrative figures and tables are included to discuss the problem in detail. The role of a Coulomb tensor interaction is investigated too. We see that the degenerate doublets are the same in both cases.

DIRAC EQUATION FOR A COULOMB SCALAR, VECTOR AND TENSOR INTERACTION

2011 ◽  
Vol 26 (06) ◽  
pp. 1011-1018 ◽  
Author(s):  
S. ZARRINKAMAR ◽  
H. HASSANABADI ◽  
A. A. RAJABI
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Exact Solutions ◽  
Pseudospin Symmetry ◽  
Spin Symmetry ◽  
Tensor Interaction ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Coulomb Term

There is now motivating experimental evidence for relativistic symmetries in nuclei and hadrons, namely pseudospin and spin symmetry limits of the Dirac equation besides the old theoretical backgrounds. The most fundamental ingredients in such studies are definitely the wave functions and energy eigenvalues. Here, having in mind the importance of the Coulomb term as well as the degeneracy-removing role of tensor interaction, we obtain the exact solutions to the problem for Coulomb scalar, vector and tensor terms in both spin and pseudospin symmetry limits. We see that, contrary to many other common cumbersome techniques, the problem is simply solved via the methodology of supersymmetric quantum mechanics.

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.

Dirac equation with CPRS potential and Cornell tensor interaction in the presence of spin and pseudospin symmetry

2020 ◽  
Vol 29 (08) ◽  
pp. 2050064
Author(s):  
Parisa Sedaghatnia ◽  
Hassan Hassanabadi ◽  
Marc de Montigny
Keyword(s):  
Dirac Equation ◽  
Nuclear Physics ◽  
Energy Levels ◽  
Pseudospin Symmetry ◽  
Tensor Interaction ◽  
Wave Functions ◽  
Nuclear Spectroscopy ◽  
Exactly Solvable

Motivated by the prominent role of tensor interactions in nuclear spectroscopy and many applications of spin and pseudospin symmetry in hadronic and nuclear physics, we solve the Dirac equation with a CPRS potential and a Cornell tensor interaction, in the spin and pseudospin symmetry limits, by using the quasi-exactly solvable method. We obtain explicitly the wave functions for the two lowest energy levels, both for spin and pseudospin symmetry. We also discuss the degeneracy of the system.

DKP EQUATION UNDER A VECTOR HULTHÉN-TYPE POTENTIAL: AN APPROXIMATE SOLUTION

2011 ◽  
Vol 26 (22) ◽  
pp. 1621-1629 ◽  
Author(s):  
S. ZARRINKAMAR ◽  
A. A. RAJABI ◽  
H. RAHIMOV ◽  
H. HASSANABADI
Keyword(s):  
Quantum Mechanics ◽  
Approximate Solution ◽  
Analytical Solutions ◽  
Hulthén Potential ◽  
Dkp Equation ◽  
Hulthen Potential ◽  
Approximate Analytical Solutions ◽  
Supersymmetry Quantum Mechanics ◽  
Type Potential

Approximate analytical solutions of Duffin–Kemmer–Petiau equation are obtained for a vector Hulthén potential. The solutions are reported for any J-state using an elegant approximation and methodology of supersymmetry quantum mechanics.

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.

AN APPROXIMATE SOLUTION OF THE DIRAC EQUATION FOR HYPERBOLIC SCALAR AND VECTOR POTENTIALS AND A COULOMB TENSOR INTERACTION BY SUSYQM

2011 ◽  
Vol 26 (36) ◽  
pp. 2703-2718 ◽  
Author(s):  
H. HASSANABADI ◽  
E. MAGHSOODI ◽  
S. ZARRINKAMAR ◽  
H. RAHIMOV
Keyword(s):  
Approximate Solution ◽  
Dirac Equation ◽  
Significant Role ◽  
Tensor Interaction ◽  
Nuclear Spectroscopy ◽  
Quantum Mechanical ◽  
Vector Potentials ◽  
Analytical Scheme ◽  
Hyperbolic Form

Based on the significant role of spin and pseudospin symmetries in hadron and nuclear spectroscopy, we have investigated Dirac equation under scalar and vector potentials of cotangent hyperbolic form besides a Coulomb tensor interaction via an approximate analytical scheme. The considered potential for small potential parameter resembles the well-established Kratzer potential. In addition, we see how the tensor term removes the degeneracy of doublets. After an acceptable approximation, namely a Pekeris-type one, we see that the problem is simply solved via the quantum mechanical idea of supersymmetry without having to deal with the cumbersome, complicated and time-consuming numerical programming.

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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