Abstract
We consider a system of two arbitrary quantum particles on a three-dimensional lattice with some dispersion functions (describing particle transport from a site to a neighboring site). The particles interact via an attractive potential at only the nearest-neighbor sites. We study how the number of eigenvalues of a family of operators h(k) depends on the particle interaction energy and the total quasimomentum \(k \in \mathbb{T}^3\), where \(\mathbb{T}^3\) is a three-dimensional torus. We find the conditions under which the operator h(0) has a double or triple virtual level at zero depending on the particle interaction energy.
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