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On the essential spectrum of quantum waveguides
Author(s) -
Rabinovich V.S.,
CastilloPérez R.,
UrbanoAltamirano F.
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2623
Subject(s) - essential spectrum , mathematics , spectrum (functional analysis) , bounded function , quantum , domain (mathematical analysis) , limit (mathematics) , boundary (topology) , boundary value problem , schrödinger's cat , mathematical analysis , class (philosophy) , series (stratigraphy) , schrödinger equation , continuous spectrum , spectral density , quantum mechanics , physics , artificial intelligence , computer science , paleontology , statistics , biology
The main aim of the paper is the study of essential spectra of electromagnetic Schrödinger operators with variable potentials in cylindric domains Π = Ω × R , where Ω ⊂ 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. Copyright © 2012 John Wiley & Sons, Ltd.