Research demonstrates isolated points as simple eigenvalues in two-particle systems, suggesting potential for positive eigenvectors.
In this paper, it is established that if the lower edge of the spectrum is an isolated point of the Schrodinger operator of a system of two particles on a lattice, then it is a simple eigenvalue and a strictly positive eigenvector corresponds to it, under certain conditions with respect to the dispersion functions and potential.
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Kuljanov et al. (2025) studied this question.
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