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Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 165, Number 1, Pages 119–133
DOI: https://doi.org/10.4213/tmf6566 (Mi tmf6566) 		 
This article is cited in 9 scientific papers (total in 9 papers)

A discrete Schrödinger operator on a graph

Yu. P. Chuburin

Physico-Technical Institute, Ural Branch, RAS, Izhevsk, Russia
Full-text PDF (434 kB) Citations (9)
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DOI: https://doi.org/10.4213/tmf6566
Abstract: We consider the discrete Schrödinger operator on the graph obtained in the strong-coupling approximation from the standard electron Schrödinger operator in the system composed of a quantum wire and quantum dot. We investigate the general spectral properties of this operator and the problem of the existence and behavior of the eigenvalues and resonances depending on the small coupling constant. We study the scattering problem for weak potentials in the stationary approach.
Keywords: discrete Schrödinger operator, spectrum, eigenvalue, resonance, scattering problem, quantum wire.
Received: 14.01.2010
English version:
Theoretical and Mathematical Physics, 2010, Volume 165, Issue 1, Pages 1335–1347
DOI: https://doi.org/10.1007/s11232-010-0112-5
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yu. P. Chuburin, “A discrete Schrödinger operator on a graph”, TMF, 165:1 (2010), 119–133; Theoret. and Math. Phys., 165:1 (2010), 1335–1347
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:95
    First page:28
     
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