|
This article is cited in 2 scientific papers (total in 2 papers)
Existence condition of an eigenvalue of the three particle Schrödinger operator on a lattice
J. I. Abdullaeva, A. M. Khalkhuzhaevb, T. H. Rasulovc a Samarkand State University, 15 University blv., Samarkand, 140104 Republic of Uzbekistan
b V.I.Romanovskiy Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, 15 University blv., Samarkand, 140104 Republic of Uzbekistan
c Bukhara State University, 11 M. Ikbol str., Bukhara, 200100 Republic of Uzbekistan
Abstract:
We consider the three-particle discrete Schrödinger operator $H_{\mu,\gamma}(\mathbf{K}),$ $\mathbf{K}\in\mathbb{T}^3$ associated to a system of three particles (two particle are fermions with mass $1$ and third one is an another particle with mass $m=1/\gamma<1$ ) interacting through zero range pairwise potential $\mu>0$ on the three-dimensional lattice $\mathbb{Z}^3.$ It is proved that for $\gamma \in (1,\gamma_0)$ ($\gamma_0\approx 4,7655$) the operator $H_{\mu,\gamma}(\boldsymbol{\pi}),$ $\boldsymbol{\pi}=(\pi,\pi,\pi),$ has no eigenvalue and has only unique eigenvalue with multiplicity three for $\gamma>\gamma_0$ lying right of the essential spectrum for sufficiently large $\mu.$
Keywords:
Schrödinger operator on a lattice, Hamiltonian, zero-range, fermion, eigenvalue, quasimomentum, invariant subspace, Faddeev operator.
Received: 29.03.2023 Revised: 07.05.2023 Accepted: 29.05.2023
Citation:
J. I. Abdullaev, A. M. Khalkhuzhaev, T. H. Rasulov, “Existence condition of an eigenvalue of the three particle Schrödinger operator on a lattice”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 9, 3–19
Linking options:
https://www.mathnet.ru/eng/ivm9930 https://www.mathnet.ru/eng/ivm/y2023/i9/p3
|
Statistics & downloads: |
Abstract page: | 59 | Full-text PDF : | 10 | References: | 15 | First page: | 2 |
|