# Observability for the Schrödinger Equation: an Optimal Transportation Approach

Abstract : We establish an observation inequality for the Schr\"odinger equation on $\bR^d$, uniform in the Planck constant $\hbar\in[0,1]$. The proof is based on the pseudometric introduced in [F. Golse, T. Paul, Arch. Rational Mech. Anal. \textbf{223} (2017), 57--94]. This inequality involves only effective constants which are computed explicitly in their dependence in $\hbar$ and all parameters involved.
Keywords :
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-03136861
Contributor : Thierry Paul Connect in order to contact the contributor
Submitted on : Wednesday, February 10, 2021 - 12:06:55 AM
Last modification on : Saturday, December 4, 2021 - 4:09:31 AM
Long-term archiving on: : Tuesday, May 11, 2021 - 6:09:58 PM

### Files

SchroObser5.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-03136861, version 1

### Citation

François Golse, Thierry Paul. Observability for the Schrödinger Equation: an Optimal Transportation Approach. 2021. ⟨hal-03136861⟩

### Metrics

Les métriques sont temporairement indisponibles