On Reducibility of Schrodinger Equations with Quasiperiodic in Time Potentials

We prove that a linear d-dimensional Schrodinger equation with an x-periodic and t-quasiperiodic potential reduces to an autonomous equation for most values of the frequency vector. The reduction is made by means of a non-autonomous linear transformation of the space of x-periodic functions. This transformation is a quasiperiodic function of t.