Approximation solution of the Dirac equation with position-dependent mass for the generalized Hulthén potential

The one-dimensional Dirac equation with position-dependent mass is approximately solved for the generalized Hulthén potential in the case of the smooth step mass distribution. The relativistic energy spectrum and two-component spinor wavefunctions are obtained by the function analysis method. Some interesting results including the standard one-dimensional Hulthén and Woods–Saxon potentials are also discussed.