Model of the effective separable potential in the problem of three one-dimensional quantum particles

TL;DR

This paper develops an effective model to analyze the asymptotic behavior of three one-dimensional quantum particles interacting via short-range attractive potentials, aiding in understanding their scattering solutions.

Contribution

It introduces a new effective model specifically designed for the asymptotic analysis of three-particle scattering in one dimension with finite attractive interactions.

Findings

The model accurately describes the asymptotic solutions.

It simplifies the analysis of complex three-particle scattering problems.

The approach reduces the discrepancy in the Schrödinger equation for these systems.

Abstract

The goal of this paper is to construct an effective model for studying the asymptotic solution of the scattering problem of three one-dimensional quantum particles with finite (short-range) attractive pair potentials. The asymptotic nature of the solution is defined by the rapid decrease in its discrepancy in the Schr\"odinger equation.