Summary: A model of localization based on the Witten Hamiltonian of supersymmetric quantum mechanics is considered. The case where the superpotential \(\phi (x)\) is a random telegraph process is solved exactly. Both the localization length and the density of states are obtained analytically. A detailed study of the low energy behaviour is presented. Analytical and numerical results are presented in the case where the intervals over which \(\phi (x)\) is kept constant are distributed according to a broad distribution. Various applications of this model are considered.