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On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice

On three-dimensional lattice we consider a system of three quantum particles (two of them are identical (fermions) and the third one is of another nature) that interact with the help of paired short-range gravitational potentials. We prove the finiteness of a number of bound states of respective Sch...

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Main Authors: Muminov, M. E., Shermatova, Y. M.
Format: Article
Published: Allerton Press Incorporation 2016
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/70094/
http://dx.doi.org/10.3103/S1066369X16010035
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spelling my.utm.700942017-11-22T00:45:13Z http://eprints.utm.my/id/eprint/70094/ On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice Muminov, M. E. Shermatova, Y. M. QA Mathematics On three-dimensional lattice we consider a system of three quantum particles (two of them are identical (fermions) and the third one is of another nature) that interact with the help of paired short-range gravitational potentials. We prove the finiteness of a number of bound states of respective Schrödinger operator in a case, when potentials satisfy some conditions and zero is a regular point for two-particle sub-Hamiltonian. We find a set of values for particles masses values such that Schrödinger operator may have only finite number of eigenvalues lying to the left of essential spectrum. Allerton Press Incorporation 2016 Article PeerReviewed Muminov, M. E. and Shermatova, Y. M. (2016) On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice. Russian Mathematics, 60 (1). pp. 22-29. ISSN 1066-369X http://dx.doi.org/10.3103/S1066369X16010035 DOI:10.3103/S1066369X16010035
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
topic QA Mathematics
spellingShingle QA Mathematics
Muminov, M. E.
Shermatova, Y. M.
On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice
description On three-dimensional lattice we consider a system of three quantum particles (two of them are identical (fermions) and the third one is of another nature) that interact with the help of paired short-range gravitational potentials. We prove the finiteness of a number of bound states of respective Schrödinger operator in a case, when potentials satisfy some conditions and zero is a regular point for two-particle sub-Hamiltonian. We find a set of values for particles masses values such that Schrödinger operator may have only finite number of eigenvalues lying to the left of essential spectrum.
format Article
author Muminov, M. E.
Shermatova, Y. M.
author_facet Muminov, M. E.
Shermatova, Y. M.
author_sort Muminov, M. E.
title On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice
title_short On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice
title_full On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice
title_fullStr On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice
title_full_unstemmed On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice
title_sort on finiteness of discrete spectrum of three-particle schrödinger operator on a lattice
publisher Allerton Press Incorporation
publishDate 2016
url http://eprints.utm.my/id/eprint/70094/
http://dx.doi.org/10.3103/S1066369X16010035
_version_ 1643656093061087232
score 13.160551

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