Geodesic
Spectral properties of two particle Hamiltonian on one-dimensional lattice
Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 99-107

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We consider a system of two arbitrary quantum particles on a one-dimensional lattice with special dispersion functions (describing site-to-site particle transport), where the particles interact by a chosen attraction potential. We study how the number of eigenvalues of the family of the operators $h(k)$ depends on the particle interaction energy and the total quasimomentum $k\in\mathbb T$ (where $\mathbb T$ is a one-dimensional torus). Depending on the particle interaction energy, we obtain conditions for existence of multiple eigenvalues below the essential spectrum of operator $h(k)$.
Keywords: two-particle Hamiltonian on one dimensional lattice, eigenvalue, multiple eigenvalue. 
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     title = {Spectral properties of two particle {Hamiltonian} on one-dimensional lattice},
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M. E. Muminov; A. M. Khurramov. Spectral properties of two particle Hamiltonian on one-dimensional lattice. Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 99-107. http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a7/