SINGULAR SUPERPOTENTIALS IN SUPERSYMMETRIC QUANTUM-MECHANICS

In the framework of supersymmetric quantum mechanics, we analyze the general problem of singular superpotentials, explicit breaking of supersymmetry, negative energy states and unpaired positive energy eigenstates. Singular superpotentials are systematically generated from the excited state wave functions of any given potential. Several special examples resulting from this procedure have been previously considered in the literature. Our approach provides a physical, intuitive understanding for the appearance of negative energy states and the presence or lack of degeneracy in the eigenvalue spectra of the supersymmetric partner potentials.