  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.
