SUPERSYMMETRY AND THE HARTMANN POTENTIAL OF THEORETICAL CHEMISTRY

An exactly solvable ring-shaped potential in quantum chemistry given b y V = eta sigma(2) epsilon(0)(2a(0)/r - eta a(0)(2)/r(2)sin(2) theta) was introduced by Hartmann in 1972 to describe ring-shaped molecules l ike benzene. In this article, the supersymmetric features of the Hartm ann 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 supe rsymmetric quantum mechanics (SUSYQM) on the half-line [0, infinity). A reformulation of SUSYQM in the full line (-infinity, infinity) is su bsequently developed. It is found that the second formulation makes a connection between states having the same quantum number L but differe nt 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 quan tum number L.