Formulation of quantum effects by using a complex‐valued equivalent circuit

Abstract

AbstractDue to the miniaturization of electronic devices, the establishment of the formation of quantum effects and the design methodology of quantum effect devices such as superlattices is becoming important.In this paper, it is attempted to consider the one‐dimensional scattering problem such as the scattering of an electron wave at the step potential and the tunneling effect at the potential barrier by a circuit theory. In other words, noting that the Schrödinger equation with time‐dependent terms contains complex coefficients, imaginary resistances, which are lossless elements, are introduced into its equivalent circuit.As a result, it has been shown that the circuit corresponds to a lossless transmission line when the electron energy is larger than the potential and that the circuit can be represented by a lumped constant circuit using reactant devices inside the potential barrier. In addition, if the electron scattering phenomenon corresponds to the circuit voltage, the conservation law of the probability can be represented by the effective power, and the transmission circuit theory is effective for the quantum effect phenomena. Furthermore, it has also been confirmed that the resonant tunneling effect and the eigenenergies of the single quantum well can be calculated by our method.