Wave function asymptotics for scattering of three-particles with Coulomb interaction

TL;DR

This paper develops the asymptotic behavior of the wave function in three-particle Coulomb scattering, using hyperspherical functions and direct asymptotic methods to analyze the Schrödinger equation.

Contribution

It introduces a new approach to derive the coordinate asymptotics of the wave function for three-particle Coulomb scattering using hyperspherical functions.

Findings

Wave function asymptotics are explicitly constructed for three-particle Coulomb scattering.

Reduction of the Schrödinger equation to a system of one-dimensional equations is achieved.

Asymptotic solutions are obtained through direct asymptotic methods.

Abstract

The coordinate asymptotics of the wave function for the problem of scattering of three particles with Coulomb interaction is constructed. Representation of hyperspherical functions is used to reduce the Schr\"odinger equation to a system of partial wave one-dimensional equations. Asymptotic solutions of this system are constructed by direct asymptotic methods.