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

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

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Official URL: http://dx.doi.org/10.3103/S1055134415030013

Abstract

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.

Item Type:Article
Uncontrolled Keywords:three-particle system on a lattice, Schrödinger operator, essential spectrum, discrete spectrum, compact operator
Subjects:A General Works
ID Code:58687
Deposited By: Haliza Zainal
Deposited On:04 Dec 2016 12:07
Last Modified:22 Feb 2017 12:13

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