The role of shape invariance potentials in the relativistic quantum mechanics

The point canonical transformation in non-relativistic quantum mechanics is applied as an algebraic method to obtain the solutions of the Dirac equation with spherical symmetry electromagnetic potentials. We want to show that some of the non-relativistic solvable potentials with shape-invariant symmetry can be related to the radial Dirac equation. Using this method, the idea of supersymmetry and shape invariance can be expanded to the relativistic quantum mechanics. The spinor wave functions for some of the obtained four-component electromagnetic potential are given in terms of special functions such as Jacobi, generalized Laguerre and Hermite polynomials. The relativistic bound-states spectrum for each case is also calculated in terms of the bound-states spectrum of the solvable potentials.