An $su(1,1)$ algebraic approach for the relativistic Kepler-Coulomb problem

TL;DR

This paper employs an $su(1,1)$ algebraic framework to analyze the relativistic Kepler-Coulomb problem, deriving energy spectra and ground states through Lie algebra representations.

Contribution

It introduces a novel algebraic approach using $su(1,1)$ Lie algebra to solve the relativistic Kepler-Coulomb problem, providing new insights into its spectral properties.

Findings

Derived the energy spectrum of the relativistic Kepler-Coulomb system.

Constructed $su(1,1)$ algebraic operators for the problem.

Identified the supersymmetric ground state.

Abstract

We apply the Schr\"odinger factorization method to the radial second-order equation for the relativistic Kepler-Coulomb problem. From these operators we construct two sets of one-variable radial operators which are realizations for the $su(1,1)$ Lie algebra. We use this algebraic structure to obtain the energy spectrum and the supersymmetric ground state for this system.