Ufa Mathematical Journal
    Volume 6, Number 4, pp. 99-107

    Spectral properties of two particle Hamiltonian on one-dimensional lattice

    Khurramov A.M., Muminov M.I.


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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 operator family $h(k)$ depends on the particle interaction energy and the total quasimomentum $k\in \mathbb{T}$ (where $\mathbb{T}$ is a one-dimensional torus). Subject to the particle interaction energy, we obtain conditions for existence of multiple eigenvalues below the essential spectrum of operator $h(k)$.