Solutions of the spatially-dependent mass Dirac equation with the spin and pseudospin symmetry for the Coulomb-like potential

Sever, Ramazan
We study the effect of spatially-dependent mass function over the solution of the Dirac equation with the Coulomb potential in the (3 + 1)-dimensions for any arbitrary spin-orbit kappa state. In the framework of the spin and pseudospin symmetry concept, the analytic bound state energy eigenvalues and the corresponding upper and lower two-component spinors of the two Dirac particles are obtained by means of the Nikiforov-Uvarov method, in closed form. This physical choice of the mass function leads to an exact analytical solution for the pseudospin part of the Dirac equation. The special cases kappa = +/- 1(l = (l) over bar = 0; i.e., s-wave), the constant mass and the non-relativistic limits are briefly investigated.


Solutions of the Klein Gordon equation with generalized hyperbolic potential in D-dimensions
Okorie, Uduakobong S.; Ikot, Akpan N.; Edet, C. O.; Akpan, I. O.; Sever, Ramazan; Rampho, R. (2019-09-01)
We solve the D- dimensional Klein-Gordon equation with a newly proposed generalized hyperbolic potential model, under the condition of equal scalar and vector potentials. The relativistic bound state energy equation has been obtained via the functional analysis method. We obtained the relativistic and non-relativistic ro-vibrational energy spectra for different diatomic molecules. The numerical results for these diatomic molecules tend to portray inter-dimensional degeneracy symmetry. Variations of the ener...
Solution of the nonlinear diffusion equation using the dual reciprocity boundary element method and the relaxation type time integration scheme
Meral, G (2005-03-18)
We present the combined application of the dual reciprocity boundary element method (DRBEM) and the finite difference method (FDM) with a relaxation parameter to the nonlinear diffusion equation: partial derivative u/partial derivative t = V del(2)u + p(u) at where p(u) is the nonlinear term. The DRBEM is employed to discretize the spatial partial derivatives by using the fundamental solution of the Laplace operator, keeping the time derivative and the nonlinearity as the nonhomogeneous terms in the equatio...
Approximate Pseudospin and Spin Solutions of the Dirac Equation for a Class of Exponential Potentials
Arda, Altug; Sever, Ramazan; TEZCAN, CEVDET (2010-02-01)
The Dirac equation is solved for some exponential potentials the hypergeometric-type potential, the generalized Morse potential, and the Poschl-Teller potential with any spin-orbit quantum number kappa in the case of spin and pseudospin symmetry. We have approximated for non s-waves the centrifugal term by an exponential form. The energy eigenvalue equations and the corresponding wave functions are obtained by using a generalization of the Nikiforov-Uvarov method.
Solutions of electromagnetics problems involving hundreds of millions of unknowns with parallel multilevel fast multipole algorithmt
Ergül, Özgür Salih (2009-06-05)
We present the solution of extremely large electromagnetics problems formulated with surface integral equations (SIEs) and discretized with hundreds of millions of unknowns. Scattering and radiation problems involving three-dimensional closed metallic objects are formulated rigorously by using the combined-field integral equation (CFIE). Surfaces are discretized with small triangles, on which the Rao-Wilton-Glisson (RWG) functions are defined to expand the induced electric current and to test the boundary c...
MUSTAFA, O; Sever, Ramazan (1993-01-01)
A different approach to the shifted 1/N expansion method is developed to deal with the Dirac particle trapped in a spherically symmetric potential. The main aspects of our approach are to expand the energy term in a perturbative form and to determine the parameters involved without any approximation. While the formalism is developed for spin-1/2 particles in any spherically symmetric potential, it is applied to the Coulomb case for testing. The calculations are carried out to the third-order correction of t...
Citation Formats
S. IKHDAİR and R. Sever, “Solutions of the spatially-dependent mass Dirac equation with the spin and pseudospin symmetry for the Coulomb-like potential,” APPLIED MATHEMATICS AND COMPUTATION, pp. 545–555, 2010, Accessed: 00, 2020. [Online]. Available: