THE NUMBER AND LOCATION OF EIGENVALUES OF THE TWO PARTICLE DISCRETE SCHRODINGER OPERATORS

Let 𝕋 be the one - dimensional torus. Let (𝕋) be the Hilbert space of squareintegrable functions on 𝕋. (𝕋) (𝕋) is the Hilbert space of square-integrable even functions on 𝕋. For any <em>µ; </em><em>λ</em> R and <em>k</em> ∈ the Schrodinger operator <em>H_µ</em><em>_λ</em> (<em>k</em>) is bounded and self-adjoint acting in (𝕋) as

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