On the scattering problem of three one-dimensional short-range quantum particles in the presence of bound states in pair subsystems

The scattering problem of three one-dimensional quantum particles of equal masses interacting via pair finite potentials is considered. The potential structure allows for bound states in the corresponding pairwise subsystems. The limiting values of the resolvent kernel of the Schrödinger operator are studied when the spectral parameter “sits” on the absolutely continuous spectrum, that is, on the positive semiaxis. As a result, coordinate asymptotics of the eigenfunctions of the absolutely continuous spectrum are constructed.