A Supersymmetric Treatment of a Particle Subjected to a Ring-shaped Potential

Abstract

The ring-shaped Hartmann potential $V=\eta {\sigma }^2{\epsilon }_0\left(\frac{2a_0}{r}-\frac{\eta a_0^2}{r^{2}si{n}^2\theta }\right)$ 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.

arXiv comment21 pages; uses LaTEX; to be published at the International Journal of Quantum Chemistry; hard copy available from the author upon e-mail ([email protected]) requests