The scattering problem of three one-dimensional quantum particles. The case of pair Coulomb potentials of repulsion at large distances

In the present work the quantum scattering problem for three one-dimensional particles with pair potenrials of Coulomb repulsion at large distances is considered. The coordinate asymptotics of the resolvent kernel in the so called BBK-domain is calculated, it making possible a reduction to the already solved scattering problem with short-range potentials. On the basis of the reduction the coordinate asymptotics resolvent kernel in all configuration space is constructed, with the spectral parameter sitting on the absolutely continuous spectrum. The formulas obtained allow to strictly justify the coordinate asymptotics of the absolutely continuous spectrum wave functions received in frames of the diffraction approach.