RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, Issue 1, Pages 29–34 (Mi vuu361)  

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

The scattering problem for a discrete Schrödinger operator with the “resonant” potential on the graph

L. E. Morozova

Izhevsk State Technical University, Izhevsk, Russia

Abstract: 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.

Full text: PDF file (136 kB)
References: PDF file   HTML file
UDC: 517.958+530.145.6
MSC: 81Q10, 81Q15
Received: 10.12.2012

Citation: L. E. Morozova, “The scattering problem for a discrete Schrödinger operator with the “resonant” potential on the graph”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 1, 29–34

Citation in format AMSBIB
\Bibitem{Mor13}
\by L.~E.~Morozova
\paper The scattering problem for a~discrete Schr\"odinger operator with the ``resonant'' potential on the graph
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2013
\issue 1
\pages 29--34
\mathnet{http://mi.mathnet.ru/vuu361}


Linking options:
  • http://mi.mathnet.ru/eng/vuu361
  • http://mi.mathnet.ru/eng/vuu/y2013/i1/p29

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. S. Smetanina, “Asimptotika urovnei operatora Shrëdingera dlya kristallicheskoi plenki s nelokalnym potentsialom”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:4 (2018), 462–473  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
    Number of views:
    This page:233
    Full text:85
    References:33
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019