State Solutions Of Dirac Equation Research Articles

Bound state solutions of Dirac equation: spin and pseudo-spin symmetry in the presence of the combined Manning–Rosen and Yukawa tensor potentials

Bound state solutions of Dirac equation: spin and pseudo-spin symmetry in the presence of the combined Manning–Rosen and Yukawa tensor potentials

Approximate Arbitrary k State Solutions of Dirac Equation with Improved Inversely Quadratic Yukawa Potential within Improved Coulomb-like Tensor Interaction in Deformation Quantum Mechanics Symmetries

Approximate Arbitrary k State Solutions of Dirac Equation with Improved Inversely Quadratic Yukawa Potential within Improved Coulomb-like Tensor Interaction in Deformation Quantum Mechanics Symmetries

Spin and pseudospin solutions to Dirac equation and its thermodynamic properties using hyperbolic Hulthen plus hyperbolic exponential inversely quadratic potential

In this research article, the modified approximation to the centrifugal barrier term is applied to solve an approximate bound state solutions of Dirac equation for spin and pseudospin symmetries with hyperbolic Hulthen plus hyperbolic exponential inversely quadratic potential using parametric Nikiforov–Uvarov method. The energy eigen equation and the unnormalised wave function were presented in closed and compact form. The nonrelativistic energy equation was obtain by applying nonrelativistic limit to the relativistic spin energy eigen equation. Numerical bound state energies were obtained for both the spin symmetry, pseudospin symmetry and the non relativistic energy. The screen parameter in the potential affects the solutions of the spin symmetry and non-relativistic energy in the same manner but in a revised form for the pseudospin symmetry energy equation. In order to ascertain the accuracy of the work, the numerical results obtained was compared to research work of existing literature and the results were found to be in excellent agreement to the existing literature. The partition function and other thermodynamic properties were obtained using the compact form of the nonrelativistic energy equation. The proposed potential model reduces to Hulthen and exponential inversely quadratic potential as special cases. All numerical computations were carried out using Maple 10.0 version and Matlab 9.0 version softwares respectively.

Approximate bound and scattering solutions of Dirac equation for the modified deformed Hylleraas potential with a Yukawa-type tensor interaction

Analytical bound and scattering state solutions of Dirac equation are investigated for the modified deformed Hylleraas potential with a Yukawa-type tensor interaction. The energy equation, phase shifts and normalization constants of the pseudospin and spin symmetry limits are represented. Since the modified deformed Hylleraas potential reduces to the Poschl–Teller, Hulthen and deformed Hylleraas potential, we have obtained energy equation and scattering properties of the Dirac equation for these potentials within a Yukawa-type tensor interaction. We have also reported some numerical results to show the effect of tensor interaction.

Bound state solutions of Dirac equation with radial exponential-type potentials

In this work, a direct approach for obtaining analytical bound state solutions of the Dirac equation for radial exponential-type potentials with spin and pseudospin symmetry conditions within the frame of the Green and Aldrich approximation to the centrifugal term is presented. The proposal is based on the relation existing between the Dirac equation and the exactly solvable Schrödinger equation for a class of multi-parameter exponential-type potential. The usefulness of the present approach is exemplified by considering some known specific exponential-type potentials which are obtained as particular cases from our proposal. That is, instead of solving the Dirac equation for a special exponential potential, by means of a specialized method, the energy spectra and wave functions are derived directly from the proposed approach. Beyond the applications considered in this work, our proposition could be used as an alternative way in the search of bound state solutions of the Dirac equation for other potentials as well as it can be easily adapted to other approximations to the centrifugal term.

Bound state solutions of Dirac equation with repulsive scalar linear potential

Abstract

Exact Solution of Dirac Equation for q-Deformed Trigonometric Scarf potential with q-Deformed Trigonometric Tensor Coupling Potential for Spin and Pseudospin Symmetries Using Romanovski Polynomial

The bound state solutions of Dirac equation for q-deformed trigonometric Scarf potential with q-deformed trigonometric cotangent and cosecant tensor coupling potential under spin and pseudospin symmetric limits are investigated using Supersymmetric Quantum Mechanics (SUSY QM) method. The new tensor potentials proposed is inspired by superpotential form in SUSY quantum mechanics. The Dirac equations for Scarf potential coupled by new tensor potential in the pseudospin and spin symmetric cases reduce to Schrodinger type equations for shape invariant potential since the proposed new potentials are equivalent to the superpotential of q-deformed trigonometric Scarf potential. The relativistic wave functions are exactly obtained by using SUSY operator method and the relativistic energy equation are exactly obtained by using SUSY method and the idea of shape invariance in the approximation scheme of centrifugal term. The new tensor potential causes the energy degeneracies is omit both for pseudospin and spin symmetric case.

Solution of Dirac Equation for q-Deformed Eckart Potential with Yukawa-type Tensor Interaction for Spin and Pseudospin Symmetry Using Romanovski Polynomial

The motion of a nucleon in q-deformed Eckart potential field coupled with Yukawa-type tensor potential is described by using Dirac equation. The bound state solutions of Dirac equation for q-deformed Eckart potential with Yukawa-type tensor potential under exact spin- and pseudospin-symmetric limit are obtained using finite Romanovski polynomials. The approximate relativistic energy spectra are exactly obtained within the approximation scheme of centrifugal term. The relativistic energy is negative for pseudospin symmetry and positive for spin symmetry. The radial component of Dirac spinors are obtained in terms of Romanovski polynomials under exact spin- and pseudospin-symmetric conditions. The relativistic energy spectrum for the exact spin-symmetric case reduces to non-relativistic energy spectrum in the non-relativistic limit. Received: 23 October 2013; Revised: 02 November 2013 Accepted: 10 November 2013

Spin and Pseudospin Symmetries of Dirac Equation and the Yukawa Potential as the Tensor Interaction

Considering of a tensor interaction in Dirac equation removes the degeneracy in spin and pseudospin doublets and consequently leads to results consistent with the experimental data. Here, instead of the commonly used Coulomb or linear terms, we investigate a tensor interaction of Yukawa form. We obtain arbitrary state solutions of Dirac equation under vector, scalar and tensor Yukawa potentials via a physical approximation and the Nikiforov—Uvarov methodology. The solutions are discussed in detail.

Approximate bound state solutions of Dirac equation with Hulthén potential including Coulomb-like tensor potential

We solve the Dirac equation approximately for the attractive scalar S ( r ) and repulsive vector V ( r ) Hulthén potentials including a Coulomb-like tensor potential with arbitrary spin-orbit coupling quantum number κ . In the framework of the spin and pseudospin symmetric concept, we obtain the analytic energy spectrum and the corresponding two-component upper- and lower-spinors of the two Dirac particles by means of the Nikiforov–Uvarov method in closed form. The limit of zero tensor coupling and the non-relativistic solution are obtained. The energy spectrum for various levels is presented for several κ values under the condition of exact spin symmetry in the presence or absence of tensor coupling.

Bound states for Dirac equation with Wood-Saxon potential

The s wave exact bound state solutions of Dirac equation are obtained when the Wood-Saxon -type scalar potential is not less than its vector potential.