The main aim of the paper is the study of essential spectra of electromagnetic Schrödinger operators with variable potentials in cylindric domains … D R, where R n is a bounded domain with a smooth boundary provided by admissible boundary conditions. Applying the limit operators method, we obtain explicit estimates of the essential spectrum for a wide class of quantum waveguides.We also consider a numerical example of calculations of the discrete spectrum of horizontally stratified quantum waveguides applying a method of the decomposition of solutions of spectral problems for one-dimensional Schrödinger operators as a power series with respect to the spectral parameter.

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.