Accidental degeneracies, hidden supersymmetries, and spectrum-generating superalgebras

Recently, several Hamiltonians appeared in the literature which exhibit degeneracies that do not seem to be explainable in terms of hidden symmetry groups. Such Hamiltonians are shown to constitute supersymmetric quantum-mechanical systems. The concept of spectrum-generating superalgebras is introduced and coordinate space representations of the relevant non-compact superalgebras Osp(1/2) and SU(1,1/1) are exhibited