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In the present paper, we establish a reduction theorem for linearSchr\"odinger equation with finite smooth and time-quasi-periodic potentialsubject to Dirichlet boundary condition by means of KAM technique. Moreover, itis proved that the corresponding Schr\"odinger operator possesses the propertyof pure point spectra and zero Lyapunov exponent.

A reducibility result for Schr\"odinger operator with finite smooth and time quasi-periodic potential