On some integral transforms of Coulomb functions related to three-dimensional proper Lorentz group

TL;DR

This paper explores integral transforms of Coulomb functions linked to the three-dimensional proper Lorentz group, deriving formulas that connect these functions through various integral transforms such as Fourier and Mellin.

Contribution

It introduces new formulas involving integral transforms of Coulomb functions within the context of the Lorentz group representation theory.

Findings

Derived formulas for integral transforms of Coulomb functions

Established connections between Coulomb functions and various integral transforms

Enhanced understanding of the mathematical structure of Coulomb functions in Lorentz group representations

Abstract

Considering the relationship between two bases in representation space of the three-dimensional proper Lorentz group, we derive some formulas with integrals involving Coulomb wave functions, which can be considered as Fourier, Mellin, $K$-Bessel, Hankel and Mehler-Fock transforms of these functions.