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Matematicheskie Trudy, 2010, Volume 13, Number 1, Pages 169–185 (Mi mt195)  
On the essential spectrum of a four-particle Schrödinger operator on a lattice

M. I. Muminovab, U. R. Shodieva

a A. Navoi Samarkand State University, Samarkand, Uzbekistan
b Department of Mathematics, Dogus University, Istanbul, Turkey
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Abstract: The Hamiltonian of a system of four arbitrary quantum particles with three-particle short-range interaction potentials on a three-dimensional lattice is examined. The location of the essential spectrum of this Hamiltonian is described by Faddeev's equations.
Key words: Schrödinger operator, Faddeev's equations, essential spectrum, compact operator, positive operator.
Received: 12.02.2009
English version:
Siberian Advances in Mathematics, 2011, Volume 21, Issue 4, Pages 292–303
DOI: https://doi.org/10.3103/S1055134411040079
Bibliographic databases:
Document Type: Article
UDC: 517.984
Language: Russian
Citation: M. I. Muminov, U. R. Shodiev, “On the essential spectrum of a four-particle Schrödinger operator on a lattice”, Mat. Tr., 13:1 (2010), 169–185; Siberian Adv. Math., 21:4 (2011), 292–303
Citation in format AMSBIB
\Bibitem{MumSho10}
\by M.~I.~Muminov, U.~R.~Shodiev
\paper On the essential spectrum of a~four-particle Schr\"odinger operator on a~lattice
\jour Mat. Tr.
\yr 2010
\vol 13
\issue 1
\pages 169--185
\mathnet{http://mi.mathnet.ru/mt195}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2682772}
\elib{https://elibrary.ru/item.asp?id=14646024}
\transl
\jour Siberian Adv. Math.
\yr 2011
\vol 21
\issue 4
\pages 292--303
\crossref{https://doi.org/10.3103/S1055134411040079}
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    		Математические труды Siberian Advances in Mathematics
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