Physics – Quantum Physics
Scientific paper
1996-02-08
Physics
Quantum Physics
24 pages; uses LaTex; to be published at the Theoretica Chimica Acta; hard copy available from the author upon request (use ad
Scientific paper
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 $L$.
No associations
LandOfFree
Supersymmetry and the Hartmann Potential of Theoretical Chemistry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Supersymmetry and the Hartmann Potential of Theoretical Chemistry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Supersymmetry and the Hartmann Potential of Theoretical Chemistry will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-287515