# Article

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

# Spectral properties of two particle Hamiltonian on one-dimensional lattice

Muminov M.I., Khurramov A.M.

DOI:10.13108/2014-6-4-99

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 $h(k)$.