Some years ago several families of superintegrable Hamiltonian systems lying in homogeneous spaces of SO(p, q) (spaces with constant curvature) were constructed by symmetry reduction a la Marsden-Weinstein from a free Hamiltonian system on a homogeneous space of SU(p, q).(1) In this communication we present the quantum version of some of these systems and solve the corresponding Schrodinger equation by means of a multidimensional factorization of these Hamiltonians.