Transition matrices for quantum waveguides with impurities

Abstract

We consider the electron propagation in a cylindrical quantum waveguide Π ¼ D× R where D is a bounded domain in R 2 described by the Dirichlet problem for the Schrödinger operatorVðxÞ is the transversal confinement potential, and Wðx; zÞ is the impurity potential. We construct the left and right transition matrices and give an numerical algorithm for their calculations based on the spectral parameter power series method.

Asymptotic and numerical analysis of slowly varying two-dimensional quantum waveguides

“…Most of the literature on quantum waveguides is focussed on the spectral and scattering properties of the quantum particles subjected to interaction conditions [7,[18][19][20][21][22][23][24][25][26][27][28]. Moreover, the influence of the geometry of the confinement region Π on the spectral properties of the waveguide has also been studied with emphasis on the curvature-induced bound states [25,27,[29][30][31], although other aspects have been considered [27,[32][33][34].…”

“…The motivation and advantages of using the SPPS method are that the calculation of the modes of a slowly varying waveguide with a large perturbation length requires a numerical analysis of a large number of transverse Sturm-Liouville problems, for which the SPPS method is used in this work. This method was proposed in the works [35,36] and was applied earlier for the numerical analysis of electromagnetic and acoustic stratified waveguides in the works [24,34,[37][38][39][40][41][42].…”