The system of three three-dimensional charged quantum particles: asymptotic behavior of the eigenfunctions of the continuous spectrum at infinity

TL;DR

This paper investigates the asymptotic behavior of eigenfunctions in a three-particle charged quantum system, providing insights into their behavior at infinity, which is crucial for understanding scattering processes.

Contribution

It offers a heuristic derivation of the leading order asymptotics of eigenfunctions for a three-particle charged quantum system, independent of mass and charge magnitude assumptions.

Findings

Derived the leading order asymptotics of eigenfunctions at infinity.

Showed the method's applicability regardless of mass and charge equality.

Enhanced understanding of scattering states in multi-particle quantum systems.

Abstract

The asymptotic behavior in the leading order of the continuous spectrum eigenfunctions $\Psi(\bz,\bq)$ as $|\bz|\rightarrow\infty$ for the system of three three-dimensional charged quantum particles has been obtained on the heuristic level. The equality of the masses and the equality of the absolute values of charges of particles are not crucial for the method.