Geodesic
The scattering problem for a~discrete Schr\"odinger operator with the ``resonant'' potential on the graph
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2013), pp. 29-34

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We consider a discrete Schrödinger operator on the graph, which is the Hamiltonian in the tight-binding approach of an electron in the system consisting of a quantum wire, and two embedded quantum dots. This operator describes the double-barrier resonant nanostructure, in which one of the barriers is a non-local 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 Lippmann–Schwinger scattering problem, quantum dot. 
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     author = {L. E. Morozova},
     title = {The scattering problem for a~discrete {Schr\"odinger} operator with the ``resonant'' potential on the graph},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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     year = {2013},
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L. E. Morozova. The scattering problem for a~discrete Schr\"odinger operator with the ``resonant'' potential on the graph. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2013), pp. 29-34. http://geodesic.mathdoc.fr/item/VUU_2013_1_a3/