Geodesic
Existence condition of an eigenvalue of the three particle Schr\"odinger operator on a lattice
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2023), pp. 3-19.

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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 $m=1/\gamma1$ ) 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, eigenvalue, quasimomentum, invariant subspace, Faddeev operator.
Mots-clés : fermion 
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     author = {J. I. Abdullaev and A. M. Khalkhuzhaev and T. H. Rasulov},
     title = {Existence condition of an eigenvalue of the three particle {Schr\"odinger} operator on a lattice},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
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J. I. Abdullaev; A. M. Khalkhuzhaev; T. H. Rasulov. Existence condition of an eigenvalue of the three particle Schr\"odinger operator on a lattice. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2023), pp. 3-19. http://geodesic.mathdoc.fr/item/IVM_2023_9_a0/

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