Archive of Issues
Russia Izhevsk
Section  Mathematics 
Title  The scattering problem for a discrete Schrödinger operator with the “resonant” potential on the graph 
Author(s)  Morozova L.E.^{a} 
Affiliations  Izhevsk State Technical University^{a} 
Abstract  We consider a discrete Schrödinger operator on the graph, which is the Hamiltonian in the tightbinding approach of an electron in the system consisting of a quantum wire, and two embedded quantum dots. This operator describes the doublebarrier resonant nanostructure, in which one of the barriers is a nonlocal potential. The essential and absolutely continuous spectra of this operator are described. We study the scattering problem in the stationary approach for two possible directions of particles propagation. The conditions of total reflection and total transmission are found. 
Keywords  discrete Schrödinger operator, spectrum, the LippmannSchwinger scattering problem, quantum dot 
UDC  517.958, 530.145.6 
MSC  81Q10, 81Q15 
DOI  10.20537/vm130104 
Received  10 December 2012 
Language  Russian 
Citation  Morozova L.E. The scattering problem for a discrete Schrödinger operator with the “resonant” potential on the graph, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 1, pp. 2934. 
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