Geodesic
Spectral properties of a two-particle hamiltonian on a $d$-dimensional lattice
Nanosistemy: fizika, himiâ, matematika, Tome 7 (2016) no. 5, pp. 880-887.

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A system of two arbitrary quantum particles moving on $d$-dimensional lattice interacting via some attractive potential is considered. The number of eigenvalues of the family $h(k)$ is studied depending on the interaction energy of particles and the total quasi-momentum $k\in\mathbb{T}^d$ ($\mathbb{T}^d$ – $d$-dimensional torus). Depending on the interaction energy, the conditions for $h(0)$ that has simple or multifold virtual level at 0 are found.
Keywords: two-particle hamiltonian, virtual level, multiplicity of virtual level. 
@article{NANO_2016_7_5_a9,
     author = {M. I. Muminov and A. M. Khurramov},
     title = {Spectral properties of a two-particle hamiltonian on a $d$-dimensional lattice},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {880--887},
     publisher = {mathdoc},
     volume = {7},
     number = {5},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2016_7_5_a9/}
}
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M. I. Muminov; A. M. Khurramov. Spectral properties of a two-particle hamiltonian on a $d$-dimensional lattice. Nanosistemy: fizika, himiâ, matematika, Tome 7 (2016) no. 5, pp. 880-887. http://geodesic.mathdoc.fr/item/NANO_2016_7_5_a9/