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THE EXICTENCE OF EIGENVALUES AND THE ESSENTIAL SPECTRUM OF THE TWO-PARTICLE DISCRETE SCHRÖDINGER OPERATOR ON LATTICES

S.N.Lakaev, Sh.I.Hamidov, S. Abduvayitov


We study a two-particle discrete Schrödinger operator
associated with a system of three particles moving on the three-dimensional cubic lattice depending on the interaction magnitude
and particles mass ratio
. We establish the essential spectrum of the two-particle discrete Schrödinger operator and prove the existence of eigenvalues located below the bottom of the essential spectrum of two-particle discrete Schrödinger operator
for all
, under the assumption that the bottom of the essential spectrum is a resonance (virtual level) of operator



https://doi.org/10.59251/2181-1296.v5.1351.1114

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