Group-theoretical approach to a non-central extension of the Kepler-Coulomb problem

TL;DR

This paper analytically explores a non-central extension of the 3D Kepler-Coulomb problem using group theory, deriving bound and scattering states with explicit S matrix calculations.

Contribution

It introduces a group-theoretical framework for a non-central Kepler-Coulomb extension, providing explicit solutions for bound and scattering states.

Findings

Bound states characterized by SO(7) symmetry.

Scattering states analyzed with SO(6,1) symmetry.

Explicit S matrix obtained via intertwining operators.

Abstract

Bound and scattering states of a non-central extension of the three-dimensional Kepler-Coulomb Hamiltonian are worked out analytically within the framework of the potential groups of the problem, SO(7) for bound states and SO(6,1) for scattering states. In the latter case, the S matrix is calculated by the method of intertwining operators.