The ring-shaped Hartmann potential $ V = ησ^{2} ε_{0} \left( \frac{2 a_{0}}{r} - \frac{ηa_{0}^{2}}{r^{2} sin^{2} θ} \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
[0,∞). A reformulation of SUSYQM in the full line
(−∞,∞) 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
ησ2 and quantum number
N. This is in contrast to the first formulation, which relates states with identical values of the quantum number
N and
ησ2 but different values of the quantum number
L.
The ring-shaped Hartmann potential
V=ησ2ε0(r2a0−r2sin2θηa02) was introduced in quantum chemistry to describe ring-shaped molecules like benzene. In this article, fundamental concepts of supersymmetric quantum mechanics (SUSYQM) are discussed. The energy eigenvalues and (radial) eigenfunctions of the Hartmann potential are subsequently rederived using the techniques of SUSYQM.