SINGULAR SUPERPOTENTIALS AND EXPLICIT BREAKING OF SUPERSYMMETRY

We describe a method of generating a family of supersymmetric quantum mechanics models depending on two positive integers (l,j),l > j. All of them exhibit singular superpotentials, explicit breaking of supersymmetry, a normalizable zero mode and j eigenstates with negative energy. We discuss the nodal structure of the solutions to the two supersymmetric partner Schrodinger equations. If we fix j = 1, the two Hamiltonians H- and H+ include Poschl-Teller potentials and under these circumstances the problem is solvable. Maintaining j = 1, but now letting l is-an-element-of (- infinity, infinity), we find a model similar to the ones which have been considered in the literature.