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On the spectrum of the three-particle Hamiltonian on a unidimensional lattice

On a unidimensional lattice, the Hamiltonian of a system of three arbitrary particles is considered (with dispersion relations), where the particles interact pairwise via zero-range (contact) attractive potentials.We prove that the discrete spectrum of the corresponding Schrödinger operator is finit...

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Main Authors: Aliev, N. M., Muminov, Mukhiddin É.
Format: Article
Published: Allerton Press Incorporation 2015
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/58687/
http://dx.doi.org/10.3103/S1055134415030013
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spelling my.utm.586872021-12-06T03:02:26Z http://eprints.utm.my/id/eprint/58687/ On the spectrum of the three-particle Hamiltonian on a unidimensional lattice Aliev, N. M. Muminov, Mukhiddin É. QA Mathematics On a unidimensional lattice, the Hamiltonian of a system of three arbitrary particles is considered (with dispersion relations), where the particles interact pairwise via zero-range (contact) attractive potentials.We prove that the discrete spectrum of the corresponding Schrödinger operator is finite for all values of the total quasimomentum if the masses of two particles are finite. We also prove that the discrete spectrum of the Schrödinger operator is infinite if the masses of two particles in a three-particle system are infinite. Allerton Press Incorporation 2015 Article PeerReviewed Aliev, N. M. and Muminov, Mukhiddin É. (2015) On the spectrum of the three-particle Hamiltonian on a unidimensional lattice. Siberian Advances in Mathematics, 25 (3). pp. 155-168. ISSN 1055-1344 http://dx.doi.org/10.3103/S1055134415030013 DOI:10.3103/S1055134415030013
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
Aliev, N. M.
Muminov, Mukhiddin É.
On the spectrum of the three-particle Hamiltonian on a unidimensional lattice
description On a unidimensional lattice, the Hamiltonian of a system of three arbitrary particles is considered (with dispersion relations), where the particles interact pairwise via zero-range (contact) attractive potentials.We prove that the discrete spectrum of the corresponding Schrödinger operator is finite for all values of the total quasimomentum if the masses of two particles are finite. We also prove that the discrete spectrum of the Schrödinger operator is infinite if the masses of two particles in a three-particle system are infinite.
format Article
author Aliev, N. M.
Muminov, Mukhiddin É.
author_facet Aliev, N. M.
Muminov, Mukhiddin É.
author_sort Aliev, N. M.
title On the spectrum of the three-particle Hamiltonian on a unidimensional lattice
title_short On the spectrum of the three-particle Hamiltonian on a unidimensional lattice
title_full On the spectrum of the three-particle Hamiltonian on a unidimensional lattice
title_fullStr On the spectrum of the three-particle Hamiltonian on a unidimensional lattice
title_full_unstemmed On the spectrum of the three-particle Hamiltonian on a unidimensional lattice
title_sort on the spectrum of the three-particle hamiltonian on a unidimensional lattice
publisher Allerton Press Incorporation
publishDate 2015
url http://eprints.utm.my/id/eprint/58687/
http://dx.doi.org/10.3103/S1055134415030013
_version_ 1718926034098716672
score 13.160551

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