On the essential spectrum of quantum waveguides

The main aim of the paper is the study of essential spectra of electromagnetic Schrodinger operators with variable potentials in cylindric domains = x R, where < subset of> Rn 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 Schrodinger operators as a power series with respect to the spectral parameter. Copyright (c) 2012 John Wiley & Sons, Ltd.