  We develop a new abstract derivation of the observability inequalities at two
points in time for Schr\"odinger type equations. Our approach consists of two
steps. In the first step we prove a Nazarov type uncertainty principle
associated with a non-negative self-adjoint operator $H$ on
$L^2(\mathbb{R}^n)$. In the second step we use results on asymptotic behavior
of $e^{-itH}$, in particular, minimal velocity estimates introduced by Sigal
and Soffer. Such observability inequalities are closely related to unique
continuation problems as well as controllability for the Schr\"odinger
equation.
