Spectral properties of a two-boson system on a three-dimensional lattice

This paper investigates the spectral properties of the two-particle Schrodinger operator h(k), associated with the Hamiltonian of a system of two bosons moving on a three-dimensional lattice. The operator is considered as a perturbation of the free Hamiltonian h 0 (k) with a potential v of a specific rank 10. The conditions for the existence of eigenvalues and virtual levels of h(k) are analyzed in the context of particle interactions with parameters 7, A, p, and the total quasi­momentum k € T 3 . The results show that the existence of virtual levels strongly depends on the nature of the interaction and the chosen potential. These findings are important for further understanding the dynamics of bosons and their interactions in quantum systems, and may serve as a basis for future research in this field.

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