Effects of relativity on the time-resolved tunneling of electron wave packets - art. no. 032107

We solve numerically the time-dependent Dirac equation for a quantum wave p acket tunneling through a potential barrier. We analyze the spatial probabi lity distribution of the transmitted wave packet in the context of the poss ibility of effectively superluminal peak and front velocities of the electr on during tunneling. Both the Dirac and Schrodinger theories predict superl uminal tunneling speeds. However, in contrast to the Dirac theory the Schro dinger equation allows a possible violation of causality. Based on an analy sis of the tunneling process in full temporal and spatial resolution, we in troduce an instantaneous tunneling speed that can be computed inside the po tential barrier.