On the spectrum of the Schrödinger operator for a three-particle system on a lattice

A three-particle discrete Schrödinger operator H µ,γ (K) :≡ H µ,γ (K), K = (K, K, K) ∈ 𝕋 3 , which is associated with a system of three particles (two fermions of mass 1 and one other particle of mass m = 1/γ ,) interacting via pairwise repulsive contact potentials µ > 0 on a three-dimensional lattice ℤ 3 , was analyzed. Critical values of mass ratios γs(K) and γas(K) were determined such that the operator H µ,γ (K) has no eigenvalues if γ ∈ (0, γs (K)), the operator H µ,γ (K) has a single eigenvalue if γ ∈ ( γs (K), γas(K)), and the operator H µ,γ (K) has three eigenvalues lying to the right of the essential spectrum for sufficiently large µ > 0 if γ ∈ ( γas (K), +∞).

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