Solution of Effective-Mass Dirac Equation with Scalar-Vector and Pseudoscalar Terms for Generalized Hulth\'en Potential

TL;DR

This paper derives exact bound-state solutions for the Dirac equation with a generalized Hulthén potential, considering scalar, vector, and pseudoscalar interactions, including special cases like constant mass, spin, pseudospin symmetry, and PT-symmetric potentials.

Contribution

It provides new analytical solutions for the Dirac equation with complex potential interactions and explores various symmetry cases and PT-symmetric forms.

Findings

Exact bound-state energy spectra derived.

Solutions include spin and pseudospin symmetry cases.

Energy spectra for PT-symmetric potentials analyzed.

Abstract

We find the exact bound-state solutions and normalization constant for the Dirac equation with scalar-vector-pseudoscalar interaction terms for the generalized Hulth\'{e}n potential in the case where we have a particular mass function $m(x)$. We also search the solutions for the constant mass where the obtained results correspond to the ones when the Dirac equation has spin and pseudospin symmetry, respectively. After giving the obtained results for the non-relativistic case, we search then the energy spectra and corresponding upper and lower components of Dirac spinor for the case of $PT$-symmetric forms of the present potential.