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Matematicheskie Trudy, 2012, Volume 15, Number 1, Pages 129–140 (Mi mt231)  
This article is cited in 1 scientific paper (total in 1 paper)

Lower bound states of one-particle Hamiltonians on an integer lattice

Z. E. Muminovab, U. N. Kulzhanova

a Samarkand State University, Samarkand, Uzbekistan
b Uzbekistan Academy of Sciences, Samarkand Branch, Samarkand, Uzbekistan
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Abstract: Under consideration is a Hamiltonian $H$ describing the motion of a quantum particle on a $d$-mentional lattice in an exterior field. It is proven that if $H$ has an eigenvalue at the lower bound of its spectrum then this eigenvalue is nondegenerate and the corresponding eigenfunction is strictly positive (thereby a lattice analog of the Perron–Frobenius theorem is proven).
Key words: spectral properties, one-particle Hamiltonian on a lattice, Birman–Schwinger principle, eigenvalue, strictly positive function.
Received: 16.12.2010
English version:
Siberian Advances in Mathematics, 2013, Volume 23, Issue 1, Pages 61–68
DOI: https://doi.org/10.3103/S1055134413010057
Bibliographic databases:
Document Type: Article
UDC: 517.984
Language: Russian
Citation: Z. E. Muminov, U. N. Kulzhanov, “Lower bound states of one-particle Hamiltonians on an integer lattice”, Mat. Tr., 15:1 (2012), 129–140; Siberian Adv. Math., 23:1 (2013), 61–68
Citation in format AMSBIB
\Bibitem{MumKul12}
\by Z.~E.~Muminov, U.~N.~Kulzhanov
\paper Lower bound states of one-particle Hamiltonians on an integer lattice
\jour Mat. Tr.
\yr 2012
\vol 15
\issue 1
\pages 129--140
\mathnet{http://mi.mathnet.ru/mt231}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2984680}
\elib{https://elibrary.ru/item.asp?id=17718102}
\transl
\jour Siberian Adv. Math.
\yr 2013
\vol 23
\issue 1
\pages 61--68
\crossref{https://doi.org/10.3103/S1055134413010057}
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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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