One- and two-dimensional Coulomb Green's function matrices in parabolic Sturmians basis

TL;DR

This paper develops matrix representations of Coulomb Green's functions in parabolic coordinates using square integrable basis sets, facilitating solutions to three-body Coulomb problems.

Contribution

It introduces a method to represent one- and two-dimensional Coulomb Green's functions as matrices in a parabolic Sturmian basis, advancing computational techniques for three-body Coulomb systems.

Findings

Matrix representations of Green's functions are derived.

The approach simplifies solving three-body Coulomb wave equations.

Potential applications in quantum three-body problem calculations.

Abstract

One- and two-dimensional operators which originate from the asymptotic form of the three-body Coulomb wave equation in parabolic coordinates are treated within the context of square integrable basis set. The matrix representations of Green's functions corresponding to these operators are obtained.