Supersymmetry and singular perturbations

First it is shown in an abstract framework that supersymmetric quantum theory may give rise to very singular perturbations, which make perturbation theories invalid. Then, the abstract results are applied to a model of 1-dimensional supersymmetric quantum mechanics (Witten's model) to obtain some families of singular Hamiltonians. Some concrete examples, which reveal their singularness, are discussed in detail.