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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 6, Pages 24–30 (Mi ivm9007)  
On compact distribution of two-particle Schrödinger operator on a lattice

M. I. Muminova, A. M. Khurramovb

a Chair of Mathematics of Sciences, Universiti Teknologi Malaysia, Jahor, 81310 Bahru, Malaysia
b Samarkand State University, 15 Universitetskii Blvd., Samarkand, 140101 Republic of Uzbekistan
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Abstract: We consider a system of two arbitrary quantum particles on three-dimensional lattice with certain dispersion functions (they describe a transfer of a particle from one node to another) which with the help of gravity potential interact on nearest neighboring nodes, only. We find a class of potentials such that under perturbation of two-particle operator $h(k)$, which corresponds to a system of two particles with a potential from this class, a discrete operator $h(k)$ is kept.
Keywords: two-particle Hamiltonian on a lattice, virtual level, multiplicity of virtual level, eigenvalue, discrete spectrum.
Received: 14.12.2013
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, Volume 59, Issue 6, Pages 18–22
DOI: https://doi.org/10.3103/S1066369X15060043
Bibliographic databases:
Document Type: Article
UDC: 517.984
Language: Russian
Citation: M. I. Muminov, A. M. Khurramov, “On compact distribution of two-particle Schrödinger operator on a lattice”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 6, 24–30; Russian Math. (Iz. VUZ), 59:6 (2015), 18–22
Citation in format AMSBIB
\Bibitem{MumHur15}
\by M.~I.~Muminov, A.~M.~Khurramov
\paper On compact distribution of two-particle Schr\"odinger operator on a~lattice
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 6
\pages 24--30
\mathnet{http://mi.mathnet.ru/ivm9007}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 6
\pages 18--22
\crossref{https://doi.org/10.3103/S1066369X15060043}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84938225712}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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