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Teoreticheskaya i Matematicheskaya Fizika, 1994, Volume 99, Number 1, Pages 103–120 (Mi tmf1570)  
This article is cited in 6 scientific papers (total in 6 papers)

Limits of applicability of the tight binding approximation

A. L. Mironov, V. L. Oleinik

St. Petersburg State University, Faculty of Physics
Full-text PDF (1444 kB) Citations (6)
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Abstract: The mathematical foundation of the tight binding approximation is given. Let λ0 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 λ0. We study this band when T tends to infinity.
Received: 22.02.1993
English version:
Theoretical and Mathematical Physics, 1994, Volume 99, Issue 1, Pages 457–469
DOI: https://doi.org/10.1007/BF01018800
Bibliographic databases:
Language: Russian
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://mathscinet.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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1994PU13400009}
Linking options:
  • https://www.mathnet.ru/eng/tmf1570
  • https://www.mathnet.ru/eng/tmf/v99/i1/p103
    • This publication is cited in the following 6 articles:
    1. Habib Ammari, Silvio Barandun, Ping Liu, “Applications of Chebyshev polynomials and Toeplitz theory to topological metamaterials”, Reviews in Physics, 13 (2025), 100103  crossref
    2. Habib Ammari, Francesco Fiorani, Erik Orvehed Hiltunen, “On the Validity of the Tight-Binding Method for Describing Systems of Subwavelength Resonators”, SIAM J. Appl. Math., 82:4 (2022), 1611  crossref
    3. 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
    4. 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
    5. 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
    6. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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