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 show that the observability inequality at two points in time is equivalent to the uncertainty principle given in .
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Gengsheng Wang, Ming Wang, Yubiao Zhang, Observability and unique continuation inequalities for the Schrödinger equation. J. Eur. Math. Soc. 21 (2019), no. 11, pp. 3513–3572DOI 10.4171/JEMS/908