Analytical representation of an iterative formula for a quantum wave impedance determination in a case of a piecewise constant potential

Abstract

An analytical solution for a quantum wave impedance in a case of piesewise constant potential was derived. It is in fact an analytical depiction of a well-known iterative method of a quantum wave impedance determination. The expression for a transmission probability as a function of a particle energy for an arbitrary cascad of constant potentials was obtained. The application of obtained results was illustrated on a system of doublewell/barrier structures.

Finite periodic $δ-δ'$ comb

“…In our previous papers [19,20,21,22,23,24,25,26] we demonstarted how a quantum wave impedance method can be applied to the investigation of infinite and semi-infinite periodic structures which contain both a piesewise constant potential and zero-range singular potentials, namely δ and δ − δ while in [27] we developed an approach to a study of systems with a complicated geometry of a potential. Next step we have done in [28], where a technique of theoretical study of finit periodic structures using the advantures of both transfer matrix approach and a quantum wave impedance method was proposed.…”