Global unique continuation from a half space for the Schrödinger equation

We obtain a global unique continuation result for the differential inequality |(i∂t+Δ)u|⩽|V(x)u| in Rn+1. This is the first result on global unique continuation for the Schrödinger equation with time-independent potentials V(x) in Rn. Our method is based on a new type of Carleman estimates for the operator i∂t+Δ on Rn+1. As a corollary of the result, we also obtain a new unique continuation result for some parabolic equations.