Abstract The problem of a particle moving in a two-valued random potential occurred in a recent paper by Pomeau. The exact time-dependent solution is here obtained for a quadratic potential by two different methods. The first method treats the problem as a stochastic differential equation and leads to the characteristic function of the probability distribution of the particle coordinate. In the second method the equation for the joint probability density of particle and potential is solved, which leads to the temporal Laplace transform of the distribution. The spectral properties of the evolution operator are examined.