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Nanosystems: Physics, Chemistry, Mathematics, 2015, Volume 6, Issue 6, Pages 762–766
DOI: https://doi.org/10.17586/2220-8054-2015-6-6-762-766 (Mi nano990) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The Green function for simplest quantum graphs

K. K. Sabirova, U. A. Aminovb, Kh. Sh. Saparovb, M. K. Karimovb, Kh. E. Abdikarimovb

a Physics Faculty, National University of Uzbekistan, Tashkent, Uzbekistan
b Urganch State University, Urganch, Uzbekistan
Full-text PDF (279 kB) Citations (1)
DOI: https://doi.org/10.17586/2220-8054-2015-6-6-762-766
Abstract: We treat the problem of the Green function for quantum graphs by focusing on such topologies as star and tree graphs. The exact Green function for the Schrödinger equation on primary star graphs is derived in the form of 3$\times$3 – matrix using the vertex boundary conditions providing continuity and current conservation. Extension of the approach for the derivation for the Green function on tree graph is presented. Possible practical applications of the obtained results are discussed.
Keywords: quantum graphs, Green function, vertex boundary conditions.
Received: 01.11.2015
Bibliographic databases:
Document Type: Article
PACS: 03.65.Ge, 02.30.Ik
Language: English
Citation: K. K. Sabirov, U. A. Aminov, Kh. Sh. Saparov, M. K. Karimov, Kh. E. Abdikarimov, “The Green function for simplest quantum graphs”, Nanosystems: Physics, Chemistry, Mathematics, 6:6 (2015), 762–766
Citation in format AMSBIB
\Bibitem{SabAmiSap15}
\by K.~K.~Sabirov, U.~A.~Aminov, Kh.~Sh.~Saparov, M.~K.~Karimov, Kh.~E.~Abdikarimov
\paper The Green function for simplest quantum graphs
\jour Nanosystems: Physics, Chemistry, Mathematics
\yr 2015
\vol 6
\issue 6
\pages 762--766
\mathnet{http://mi.mathnet.ru/nano990}
\crossref{https://doi.org/10.17586/2220-8054-2015-6-6-762-766}
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\elib{https://elibrary.ru/item.asp?id=25064799}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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