On the Number of Eigenvalues of the Lattice Model Operator in One-Dimensional Case

Abstract

It is considered a model operator $$h_{\mu}(k),$$ $$k\in\mathbb{T}\equiv(-\pi,\pi]$$ , corresponding to the Hamiltonian of systems of two arbitrary quantum particles on a one-dimensional lattice with a special dispersion function that describes the transfer of a particle from one site to another interacting by a some short-range attraction potential $$v_{\mu}$$ , $$\mu=(\mu_{0},\mu_{1},\mu_{2},\mu_{3})\in\mathbb{R}^{4}_{+}$$ . The number of eigenvalues of the operator $$h_{\mu}(k),$$ $$k\in\mathbb{T}$$ depending on the energy of the particle interaction vector $$\mu\in\mathbb{R}^{4}_{+}$$ and the total quasi-momentum $$k\in\mathbb{T}$$ is studied.

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DOI

10.1134/s1995080222050109

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