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.

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.

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.

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.

EXACT SOLUTIONS OF DIRAC EQUATION FOR A NEW SPHERICALLY ASYMMETRICAL SINGULAR OSCILLATOR

2010 ◽  
Vol 25 (33) ◽  
pp. 2849-2857 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Vector Potential ◽  
State Energy ◽  
Energy Levels ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Exact Bound ◽  
Spinor Wave

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of scalar and vector spherically asymmetrical singular oscillators. This is done provided that the vector potential is equal to the scalar potential. The spinor wave functions and bound state energy levels are presented. The case V(r) = -S(r) is also considered.

Pseudospin symmetry of the Dirac equation for a Möbius square plus Mie type potential with a Coulomb-like tensor interaction via SUSYQM

2014 ◽  
Vol 38 (1) ◽  
pp. 013101 ◽  
Author(s):  
Akpan N. Ikot ◽  
S. Zarrinkamar ◽  
Eno J. Ibanga ◽  
E. Maghsoodi ◽  
H. Hassanabadi
Keyword(s):  
Dirac Equation ◽  
Pseudospin Symmetry ◽  
Tensor Interaction ◽  
Type Potential

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.

scholarly journals Exact Solutions of a Class of Double-Well Potentials: Algebraic Bethe Ansatz

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
M. Baradaran ◽  
H. Panahi
Keyword(s):  
Bethe Ansatz ◽  
Numerical Evaluation ◽  
Energy Levels ◽  
Algebraic Approach ◽  
Wave Functions ◽  
Algebraic Equations ◽  
Ansatz Method ◽  
Exact Solvability ◽  
Exactly Solvable ◽  
Bistable Potential

Applying the Bethe ansatz method, we investigate the Schrödinger equation for the three quasi-exactly solvable double-well potentials, namely, the generalized Manning potential, the Razavy bistable potential, and the hyperbolic Shifman potential. General exact expressions for the energies and the associated wave functions are obtained in terms of the roots of a set of algebraic equations. Also, we solve the same problems using the Lie algebraic approach of quasi-exact solvability through the sl(2) algebraization and show that the results are the same. The numerical evaluation of the energy spectrum is reported to display explicitly the energy levels splitting.

scholarly journals NEW TREATMENT OF THE NONCOMMUTATIVE DIRAC EQUATION WITH A COULOMB POTENTIAL

2012 ◽  
Vol 27 (19) ◽  
pp. 1250100 ◽  
Author(s):  
LAMINE KHODJA ◽  
SLIMANE ZAIM
Keyword(s):  
Magnetic Field ◽  
Field Equation ◽  
Hydrogen Atom ◽  
Dirac Equation ◽  
Hyperfine Structure ◽  
Coulomb Potential ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
New Treatment

Using the approach of the modified Euler–Lagrange field equation together with the corresponding Seiberg–Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative modification to the energy levels and the possible new transitions. In the nonrelativistic limit a general form of the Hamiltonian of the hydrogen atom is obtained, and we show that the noncommutativity plays the role of spin and magnetic field which gives the hyperfine structure.

scholarly journals Relativistic symmetries of Schioberg and general Manning-Rosen potentials and the effects of tensor coupling

2013 ◽  
Vol 37 (1) ◽  
pp. 1-17
Author(s):  
A. N. Ikot ◽  
E. Maghsoodi ◽  
C. N. Isonguyo ◽  
S. Zarrinkamar ◽  
H. Hassanabadi
Keyword(s):  
Dirac Equation ◽  
Potential Energy ◽  
Closed Form ◽  
Bound State ◽  
Tensor Interaction ◽  
Numerical Results ◽  
Wave Functions ◽  
Tensor Coupling ◽  
Energy Equations ◽  
Rosen Potential

Abstract In this paper we solve the Dirac equation with Schioberg and general Manning- Rosen potentials including the Coulomb-like tensor interaction. The approximate analytical bound state solutions of the Dirac equation with the Schioberg and Manning-Rosen potential, energy equations and the corresponding unnormalized wave functions are obtained in a closed form using SUSYQM. We have also reported the numerical results to show the effect of the tensor interaction.

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