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Physica Scripta

Approximate $\kappa$ -state solutions of the Dirac equation in spatially dependent mass for the Eckart potential including the Yukawa tensor interaction

Sameer M. Ikhdair

Published Nov 21, 2013• 8 citations
Publisher

Abstract

We investigate the analytical approximation to arbitrary -state solutions of the Dirac equation with the position-dependent mass particle in the Eckart potential including the Yukawa tensor interaction in the framework of a parametric Nikiforov–Uvarov method. By taking a proper approximation to deal with the centrifugal term, the analytical relativistic energy eigenvalues and the corresponding normalized two-spinor components of the wave function are obtained in closed form. The relativistic and non-relativistic bound state solutions for some special cases, such as the Hulthén potential and the generalized Morse potential, are easily obtained from our general solution.

DOI
10.1088/0031-8949/88/06/065007

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Approximate κ\kappaκ -state solutions of the Dirac equation in spatially dependent mass for the Eckart potential including the Yukawa tensor interaction
We investigate the analytical approximation to arbitrary -state solutions of the Dirac equation with the position-dependent mass particle in the Eckart potential including the Yukawa tensor interaction in the framework of a parametric Nikiforov–Uvarov method. By taking a proper approximation to deal with the centrifugal term, the analytical relativistic energy eigenvalues and the corresponding normalized two-spinor components of the wave function are obtained in closed form. The relativistic and non-relativistic bound state solutions for some special cases, such as the Hulthén potential and the generalized Morse potential, are easily obtained from our general solution.
Applying an appropriate approximation scheme to deal with the centrifugal term, pseudospin and spin symmetric solutions of the Dirac–Yukawa problem with tensor interaction are investigated based on supersymmetric quantum mechanics (SUSYQM) and shape invariance (SI) formalism. We show that the energy eigenvalues equation is simply obtained by using the methodology of SUSYQM and SI. The corresponding wave functions are obtained in terms of hypergeometric functions. Effects of tensor interaction on the bound states and eigenfunctions are also investigated numerically. Further, we compare our results with those given in the literature, which are obtained by using the Nikiforov–Uvarov and asymptotic iteration methods.
Abstract The Dirac equation, with position-dependent mass, is solved approximately for the generalized Hulthén potential with any spin-orbit quantum number κ. Solutions are obtained by using an appropriate coordinate transformation, reducing the effective mass Dirac equation to a Schrödinger-like differential equation. The Nikiforov-Uvarov method is used in the calculations to obtain energy eigenvalues and the corresponding wave functions. Numerical results are compared with those given in the literature. Analytical results are also obtained for the case of constant mass and the results are in good agreement with the literature.
We have obtained approximate bound state solutions of Schrödinger wave equation with modified quadratic Yukawa plus q-deformed Eckart potential Using Parametric Nikiforov-Uvarov (NU) method. However, we obtained numerical energy eigenvalues and un-normalized wave function using confluent hypergeometric function (Jacobi polynomial). With some modifications, our potential reduces to a well-known potential such as Poschl-Teller and exponential inversely quadratic potential. Numerical bound state energies were carried out using a well-designed Matlab algorithm while the plots were obtained using origin software. The result obtained is in agreement with that of the existing literature.