Scattering at a very high potential step

Scattering of a positive-energy wave packet at a very high potential step according to the Dirac equation. The potential energy behind the step is higher than the kinetic energy of the wave packet plus twice the rest energy.

Surprisinly, a part of the wave packet is transmitted. The transmitted part shows all the characteristic features of a positronic wave packet (a wave packet with negative kinetic energy). The lower spinor-component is larger than the upper spinor-component, and the momentum is opposite to the average velocity of the wave packet. (The unusual relation between the phase and the group velocity behind the step is nothing but the usual effect caused by a constant potential).