Effect of self-interference of an electron in motion: Analysis of nonlocality of an electron through a resonant tunneling diode

On the basis of the viewpoint that a static wave function is formed as a result of self-interference of a moving electron, we investigate the temporal behavior of an electronic wave function through a resonant tunneling diode. In order to do it, we extend the WKB method by introducing a semiclassical orbital function so that we can follow the motion of an incident electron within a semiclassical picture. Within this theory, resonant tunneling is described as self-interference of amplitudes multiply reflected between potential barriers. We show that the components of multiply reflected amplitudes arrive with time delay, and thus total transmission amplitude is built up with time. At the resonant condition, the transmission probability is unity, implying that an electron behaves as if it senses beyond the barrier where the amplitude of a wave function is zero. This paradoxical nonlocality is reasonably understood in terms of the temporal buildup of transmission amplitudes due to multiple reflection.