We give an upper bound on the vanishing order of solutions to Schrodinger equation on a compact smooth manifold. Our method is based on Carleman type inequalities, and gives a generalisation to a result of H. Donnely and C. Fefferman [DF88] on eigenfunctions. It also sharpens previous results of I. Kukavica [Kuk98].
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Laurent Bakri (2012) studied this question.