A reducibility result for Schrödinger operator with finite smooth and time quasi-periodic potential

Abstract

In the present paper, we establish a reduction theorem for linear Schrödinger equation with finite smooth and time-quasi-periodic potential subject to Dirichlet boundary condition by means of KAM technique. Moreover, it is proved that the corresponding Schrödinger operator possesses the property of pure point spectra and zero Lyapunov exponent.