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

A. M. Budylin^a, S. B. Levin^a, V. O. Toropov<sup>b

a</sup> Saint Petersburg State University
^b St. Petersburg National Research University of Information Technologies, Mechanics and Optics

Abstract: 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.

Key words and phrases: three one-dimensional quantum particle problem, Schrödinger operator resolvent, alternating Schwarz method, two-particle bound states, coordinate asymptotics of absolutely continuous spectrum eigenfunctions.

UDC: 517.9

Received: 28.09.2025