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TMF, 1994, Volume 99, Number 1, Pages 103–120 (Mi tmf1570)  

This article is cited in 4 scientific papers (total in 4 papers)

Limits of applicability of the tight binding approximation

A. L. Mironov, V. L. Oleinik

St. Petersburg State University, Faculty of Physics

Abstract: The mathematical foundation of the tight binding approximation is given. Let $\lambda _0$ be a negative energy level of a real potential $q$. Then there exists an energy band for a one-dimensional chain with period $2T$ of the identical atoms which lies near $\lambda _0$. We study this band when $T$ tends to infinity.

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English version:
Theoretical and Mathematical Physics, 1994, 99:1, 457–469

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Received: 22.02.1993

Citation: A. L. Mironov, V. L. Oleinik, “Limits of applicability of the tight binding approximation”, TMF, 99:1 (1994), 103–120; Theoret. and Math. Phys., 99:1 (1994), 457–469

Citation in format AMSBIB
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\by A.~L.~Mironov, V.~L.~Oleinik
\paper Limits of applicability of the tight binding approximation
\jour TMF
\yr 1994
\vol 99
\issue 1
\pages 103--120
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1302462}
\zmath{https://zbmath.org/?q=an:0849.34073}
\transl
\jour Theoret. and Math. Phys.
\yr 1994
\vol 99
\issue 1
\pages 457--469
\crossref{https://doi.org/10.1007/BF01018800}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994PU13400009}


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    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. V. A. Geiler, V. V. Demidov, “Spectrum of three-dimensional landau operator perturbed by a periodic point potential”, Theoret. and Math. Phys., 103:2 (1995), 561–569  mathnet  crossref  mathscinet  zmath  isi
    2. Yu. P. Chuburin, “On approximation of the “Membrane” Schrödinger operator by the “Crystal” operator”, Math. Notes, 62:5 (1997), 648–654  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. A. L. Mironov, V. L. Oleinik, “Limits of applicability of the tight binding approximation for complex-valued potential function”, Theoret. and Math. Phys., 112:3 (1997), 1157–1171  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Oleinik, VL, “Analysis of the dispersion equation for the Schrodinger operator on periodic metric graphs”, Waves in Random Media, 14:2 (2004), 157  crossref  mathscinet  zmath  adsnasa  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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