The levels of the two-particle Schrödinger operator corresponding to a crystal film

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For a two-particle Schrodinger operator considered in a cell and having a potential periodic in four variables, we establish the existence of levels (i.e., eigenvalues or resonances) in the neighborhood of singular points of the unperturbed Green’s function and derive an asymptotic formula for these levels. We prove an existence and uniqueness theorem for the solution of the corresponding Lippmann-Schwinger equation.