Observability and unique continuation inequalities for the Schrödinger equation

Abstract

In this paper, we present several observability and unique continuation inequalities for the free Schrödinger equation in the whole space. The observations in these inequalities are made either at two points in time or one point in time. These inequalities correspond to different kinds of controllability for the free Schrödinger equation. We also find that the observability inequality at two points in time is equivalent to the uncertainty principle built up in [18].