THE EXISTENCE OF BOUND STATES OF THE TWO-PARTICLE DISCRETE SCHRÖDINGER OPERATORS ON LATTICES

We consider a system of two identical bosons moving on the hypercubic lattice Zd d ≥1 and interacting through attractive short range potentials μV (μ > 0) and the two-particle Schrödinger operators H (k) = H (k) − V k ∈Td 0 μ μ associated to the system where Td is the d - dimensional torus. We study the existence of eigenvalues of H (k) k ∈Td μ depending on the potential μV and quasi-momentum of the two particles. In particular we prove the existence of ILMIY AXBOROTNOMA MATEMATIKA 2017-yil 3-son 29 eigenvalues of H (k) k ∈Td μ lying below the threshold of the essential spectrum for attracive (μ > 0) interaction.