SINGULAR SUPERPOTENTIALS AND EXPLICIT BREAKING OF SUPERSYMMETRY

Abstract

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 Schrödinger equations. If we fix j=1, the two Hamiltonians H − and H + include Pöschl-Teller potentials and under these circumstances the problem is solvable. Maintaining j=1, but now letting l ∈ (−∞, ∞), we find a model similar to the ones which have been considered in the literature.