Supertransparent potentials for the Dirac equation

An extension of the classical Darboux transformations is applied to the one-dimensional Dirac equation in order to construct von Neumann-Wigner potentials allowing embedded eigenvalues. These potentials lead to a novel type of scattering problem with a trivial S-matrix composed of vanishing reflection coefficients and a trivial transmission coefficient. Related topics like the underlying symmetry of the Dirac equation and the connection with positon solutions of nonlinear evolution equations are discussed.