Geodesic
Conditions for the existence of bound states of a two-particle Hamiltonian on a three-dimensional lattice
Nanosistemy: fizika, himiâ, matematika, Tome 13 (2022) no. 3, pp. 237-244 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Hamiltonian h of the system of two quantum particles moving on a 3-dimensional lattice interacting via some attractive potential is considered. Conditions for the existence of eigenvalues of the two-particle Schrödinger operator $h_{\mu}(k)$, $k\in\mathbb T^{3}$, $\mu\in\mathbb R$, associated to the Hamiltonian h, are studied depending on the energy of the particle interaction $\mu\in\mathbb R$ and total quasi-momentum $k\in\mathbb T^{3}$ ($\mathbb T^{3}$ – three-dimensional torus).
Keywords: two-particle Hamiltonian, invariant subspace, unitary equivalent operator, virtual level, multiplicity of virtual level, eigenvalue. 
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     author = {M. I. Muminov and A. M. Khurramov and I. N. Bozorov},
     title = {Conditions for the existence of bound states of a two-particle {Hamiltonian} on a three-dimensional lattice},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {237--244},
     year = {2022},
     volume = {13},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2022_13_3_a0/}
}
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M. I. Muminov; A. M. Khurramov; I. N. Bozorov. Conditions for the existence of bound states of a two-particle Hamiltonian on a three-dimensional lattice. Nanosistemy: fizika, himiâ, matematika, Tome 13 (2022) no. 3, pp. 237-244. http://geodesic.mathdoc.fr/item/NANO_2022_13_3_a0/