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

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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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
\Bibitem{MirOle94} \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 \mathnet{http://mi.mathnet.ru/tmf1570} \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
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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
2. Yu. P. Chuburin, “On approximation of the “Membrane” Schrödinger operator by the “Crystal” operator”, Math. Notes, 62:5 (1997), 648–654
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
4. Oleinik, VL, “Analysis of the dispersion equation for the Schrodinger operator on periodic metric graphs”, Waves in Random Media, 14:2 (2004), 157
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