Quantitative uniqueness for Schroedinger operator Laurent Bakri 35JCarleman estimatesquantitative uniqueness We give an upper bound on the vanishing order of solutions to Schr\"odinger's equation on a compact smooth manifold. Our method is based on Carleman type inequalities and gives a generalisation to a result of H. Donnelly and C. Fefferman [H. Donnelly and C. Fefferman, \textit{Nodal sets of eigenfunctions on Riemannian manifolds}, Invent. Math. \textbf{93} (1988), no. 1, 161--183] on eigenfunctions. It also sharpens previous results of I. Kukavica [I. Kukavica, \textit{Quantitative uniqueness for second-order elliptic operators}, Duke Math. J. \textbf{91} (1998), no. 2, 225--240]. Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.4713 10.1512/iumj.2012.61.4713 en Indiana Univ. Math. J. 61 (2012) 1565 - 1580 state-of-the-art mathematics http://iumj.org/access/