Scattering at a repulsive smooth potential barrier

This movie shows a wave packet with positive energy moving according to the Dirac equation. Its initial condition is roughly a Gaussian function. This wave packet hits a potential barrier that is so high that the probability for transmission is virtually zero. Hence the wave packet gets totally reflected. This behavior is quite as expected, and very similar to the behavior of a solution of the Schrödinger equation for this situation. The main difference is that the Dirac equation is compatible with the special theory of relativity. Hence no part of the wave packet moves with a velocity greater than the velocity of light.