Article
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.
DOI:10.13108/2014-6-4-99
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Article on MathNetAbstact
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 $h(k)$.