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Electrons possess both wave and particle natures. In this paper, we represent an electron on multi-stage coupled electron waveguides both by a wave function and by a probabilistic particle. We show first that time evolution of the wave function can be obtained by the combined use of the tight-binding method and two-port circuit theory. The wave function is in variable-separable form when wave propagation on the coupled electron waveguides is single mode. We present secondly that the variable separation simplifies the general Langevin equation describing behavior of the probabilistic particle. According to these two schemes, wave functions and sample particle trajectories on single and two-stage coupled electron waveguides were exemplified.

Representation of electrons on multi-stage coupled electron waveguides by waves and particles