Geodesic
Existence of the eigenvalues of a tensor sum of the Friedrichs models with rank 2 perturbation
Nanosistemy: fizika, himiâ, matematika, Tome 14 (2023) no. 2, pp. 151-157 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper we consider a tensor sum $H_{\mu,\lambda}$, $\mu,\lambda>0$ of two Friedrichs models $h_{\mu,\lambda}$ with rank two perturbation. The Hamiltonian $H_{\mu,\lambda}$ is associated with a system of three quantum particles on one-dimensional lattice. We investigate the number and location of the eigenvalues of $H_{\mu,\lambda}$. The existence of eigenvalues located respectively inside, in the gap, and below the bottom of the essential spectrum of $H_{\mu,\lambda}$ is proved.
Keywords: tensor sum, Hamiltonian, lattice, non-local interaction, Friedrichs model, eigenvalue
Mots-clés : quantum particles, perturbation. 
@article{NANO_2023_14_2_a0,
     author = {Tulkin H. Rasulov and Bekzod I. Bahronov},
     title = {Existence of the eigenvalues of a tensor sum of the {Friedrichs} models with rank 2 perturbation},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {151--157},
     year = {2023},
     volume = {14},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2023_14_2_a0/}
}
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Tulkin H. Rasulov; Bekzod I. Bahronov. Existence of the eigenvalues of a tensor sum of the Friedrichs models with rank 2 perturbation. Nanosistemy: fizika, himiâ, matematika, Tome 14 (2023) no. 2, pp. 151-157. http://geodesic.mathdoc.fr/item/NANO_2023_14_2_a0/