Applying the Dirac equation to derive the transfer matrix for piecewise constant potentials

One proposes a relativistic version of the transfer matrix method for an electron moving through a given number of rectangular barriers of arbitrary shape. It is shown that starting with the Dirac equation depending on the effective mass and by rescaling the relativistic potential, one obtains a relativistic transfer matrix which takes the traditional form in the non-relativistic limit. In this way, the non-relativistic method based on the Schrödinger equation and the relativistic approach proposed here naturally support to each other.