The parabolic Sturmian-function basis representation of the six-dimensional Coulomb Green's function

TL;DR

This paper develops a new basis set representation for the six-dimensional Coulomb Green's function using parabolic coordinates, enabling a convolution integral formulation of the resolvent for three-body Coulomb problems.

Contribution

It introduces a square integrable basis set representation of the three-body Coulomb Green's function in parabolic coordinates, facilitating computational approaches.

Findings

Green's function expressed as a convolution integral

New basis set simplifies three-body Coulomb calculations

Provides a framework for resolvent analysis in three-body systems

Abstract

The square integrable basis set representation of the resolvent of the asymptotic three-body Coulomb wave operator in parabolic coordinates is obtained. The resulting six-dimensional Green's function matrix is expressed as a convolution integral over separation constants.