Zahriddin I. Muminov, V. U. Aktamova, “The point spectrum of the three-particle Schrödinger operator for a system comprising two identical bosons and one fermion on <nobr>$\mathbb{Z}$</nobr>”, Nanosystems: Physics, Chemistry, Mathematics, 2024, Volume 15, Issue 4,Pages <nobr>438

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MATHEMATICS

The point spectrum of the three-particle Schrödinger operator for a system comprising two identical bosons and one fermion on $\mathbb{Z}$

Zahriddin I. Muminov^ab, V. U. Aktamova^c

^a Tashkent State University of Economics, 100066, Tashkent, Uzbekistan
^b Institute of Mathematics named after V.I.Romanovsky, 100174, Tashkent, Uzbekistan
^c Samarkand Institute of Veterinary Medicine, 140103, Samarkand, Uzbekistan

Abstract: We consider the Hamiltonian of a system of three quantum particles (two identical bosons and a fermion) on the one-dimensional lattice interacting by means of zero-range attractive or repulsive potentials. We investigate the point spectrum of the three-particle discrete Schrödinger operator $H(K)$, $K\in\mathbb{T}$ which possesses infinitely many eigenvalues depending on repulsive or attractive interactions, under the assumption that the bosons in the system have infinite mass.

Keywords: Schrödinger operator, dispersion functions, zero-range pair potentials, discrete spectrum, essential spectrum.

Received: 18.04.2024
Revised: 21.06.2024
Accepted: 26.06.2024

Language: English

DOI: 10.17586/2220-8054-2024-15-4-438-447