  The ring-shaped Hartmann potential $ V = \eta \sigma^{2} \epsilon_{0} \left(
\frac{2 a_{0}}{r} - \frac{\eta a_{0}^{2}}{r^{2} sin^{2} \theta} \right) $ was
introduced in quantum chemistry to describe ring-shaped molecules like benzene.
In this article, the supersymmetric features of the Hartmann potential are
discussed. We first review the results of a previous paper in which we
rederived the eigenvalues and radial eigenfunctions of the Hartmann potential
using a formulation of one-dimensional supersymmetric quantum mechanics
(SUSYQM) on the half-line $\left[ 0, \infty \right)$. A reformulation of SUSYQM
in the full line $\left( -\infty, \infty \right)$ is subsequently developed. It
is found that the second formulation makes a connection between states having
the same quantum number $L$ but different values of $\eta \sigma^{2}$ and
quantum number $N$. This is in contrast to the first formulation, which relates
states with identical values of the quantum number $N$ and $\eta \sigma^{2}$
but different values of the quantum number $L$.
