Few one-dimensional quantum particles scattering problem. The structure and asymptotics of the resolvent kernel limit values

The present work offers a new approach to the construction of the coordinate asymptotics of the Schrödinger operator resolvent kernel in the scattering problem of three one-dimensional quantum particles with short-range pair potentials. Within the framework of this approach the asymptotics of the absolutely continuous spectrum eigenfunctions of the Schrödinger operator can be constructed. In the work the possibility of the generalization of the suggested approach for the case of scattering problem of $N$ particles with arbitrary masses is discussed.