Dirac-Hulthen Problem with Position-dependent Mass in D-dimensions

TL;DR

This paper presents an approximate analytical solution to the Dirac equation with a position-dependent mass and Hulthen potential in D-dimensions, deriving energy spectra and wavefunctions with good agreement to prior studies.

Contribution

It introduces a novel approximate method for solving the Dirac equation with position-dependent mass and Hulthen potential in arbitrary dimensions.

Findings

Derived relativistic energy spectrum in D-dimensions.

Obtained wavefunctions in terms of Jacobi polynomials.

Results agree well with previous research.

Abstract

An approximate solution of the position-dependent mass Dirac equation with the Hulthen potential is obtained in $D$-dimensions within frame work of an exponential approximation of the centrifugal term. The relativistic energy spectrum is worked out using direct transformation method; the two-component spinor wavefunctions are obtained in terms of the Jacobi polynomials. Dependence of the energy levels on some parameters is discussed. The results obtained are in good agreement with previous works.