Observability for the Schrödinger Equation: an Optimal Transport Approach

Abstract

We establish an observation inequality for the Schrödinger equation on ${\mathbf{R}}^d$, uniform in the Planck constant $\hslash \in [0,1]$. The proof is based on the pseudometric introduced in [F. Golse, T. Paul, Arch. Rational Mech. Anal. 223 (2017), 57-94]. This inequality involves only effective constants which are computed explicitly in their dependence in $\hslash$ and all parameters involved.

15 pages, no figure