New approach to numerical computation of the eigenfunctions of the continuous spectrum of three-particle Schr\"odinger operator. I. One-dimensional particles, short-range pair potentials

TL;DR

This paper introduces a novel numerical method for computing eigenfunctions of the continuous spectrum in three-particle quantum systems, based on an analogy with diffraction problems, applicable to short-range potentials and extendable to long-range interactions.

Contribution

The paper proposes a new approach to three-body scattering problems using diffraction analogy, enabling more natural handling of short and long-range pair potentials.

Findings

Numerical results for short-range potentials demonstrate the method's effectiveness.

The approach can be generalized to long-range pair potentials.

The method provides a new perspective on three-particle scattering analysis.

Abstract

Basing on analogy between the three-body scattering problem and the diffraction problem of the plane wave (for the case of the short range pair potentials) by the system of six half transparent screens, we presented a new approach to the few-body scattering problem. The numerical results have been obtained for the case of the short range nonnegative pair potentials. The presented method allows a natural generalization to the case of the long range pair potentials.