Applying the Dirac equation to derive the transfer matrix for piecewise constant potentials
arXiv:cond-mat/0609450 · doi:10.1016/j.physleta.2007.02.097
Abstract
One propose 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 a suitably chosen relativistic potential, one obtains a relativistic transfer matrix which takes the correct traditional form in the non-relativistic limit.
4 pages, 1 figure