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

Abstract

We apply the Schrödinger 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.

References in corpus (3)

• The su(1,1) dynamical algebra from the Schrödinger ladder operators for N-dimensional systems: hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator
• SUSY QM, symmetries and spectrum generating algebras for two-dimensional systems
• The Biedenharn Approach to Relativistic Coulomb-type Problems

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• $SU(1,1)$ coherent states for Dirac-Kepler-Coulomb problem in $D+1$ dimensions with scalar and vector potentials
• On realizations of the Witt algebra in ${\mathbb{R}}^3$
• Generalized Version of the Creation and Annihilation Operators for the Schrödinger Equation