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

Abstract

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 symmetric electron-wave stub-filters by waves and particles

“…The diffusion coefficient and the drift term of FPE (17) and NSODE (18) are respectively given with h, m e in the Schrödinger equation and its wave function ψ(x, y, t) by [8,13] ν =h m e…”

“…Constant coefficients c n in Eqs. (13) and (15) are obtained by computing the following inner products between initial packet (24) and eigenfunctions φ n (x, y):…”

“…Time-evolution of the wave packets were computed by both analytical and numerical methods: The analytical method is to obtain time-evolving wave functions given by Eqs. (13), (14), and (15). The numerical method is to compute time-evolving wave function by FDM.…”

“…The term is obtained from the wave packet given by Eqs. (13), (14), and (15) and its partial differential coefficients with respect to x and y. The number of multiplication necessary to compute the drift term at every iteration (26) for the trajectory computation is 2N tri N ef , where N tri (= 140 or 175) and N ef (= 31) respectively denote the number of trigonometric functions to approximate an eigenfunctions and the number of eigenfunctions to approximate the initial distribution of the wave packets.…”

“…Another type of electron wave filter consists of several waveguides coupled by evanescent waves. A method of computing sample trajectories of electrons modeled as prbabolistic particles on coupled waveguides has been proposed recently [13].…”