  We obtain a global unique continuation result for the differential inequality
$|(i\partial_t+\Delta)u|\leq|V(x)u|$ in $\mathbb{R}^{n+1}$. This is the first
result on global unique continuation for the Schr\"odinger equation with
time-independent potentials $V(x)$ in $\mathbb{R}^{n}$. Our method is based on
a new type of Carleman estimates for the operator $i\partial_t+\Delta$ on
$\mathbb{R}^{n+1}$. As a corollary of the result, we also obtain a new unique
continuation result for some parabolic equations.
