# American Institute of Mathematical Sciences

September  2021, 10(3): 461-469. doi: 10.3934/eect.2020075

## A remark on the attainable set of the Schrödinger equation

 CNRS & Laboratoire interdisciplinaire Carnot de Bourgogne, UMR 6303 Université de Bourgogne Franche-Comté, 9 Av. A. Savary, 21078 Dijon Cedex, France

Received  November 2019 Revised  April 2020 Published  June 2020

We discuss the set of wavefunctions $\psi_V(t)$ that can be obtained from a given initial condition $\psi_0$ by applying the flow of the Schrödinger operator $-\Delta + V(t,x)$ and varying the potential $V(t,x)$. We show that this set has empty interior, both as a subset of the sphere in $L^2( \mathbb{R}^d)$ and as a set of trajectories.

Citation: Jonas Lampart. A remark on the attainable set of the Schrödinger equation. Evolution Equations & Control Theory, 2021, 10 (3) : 461-469. doi: 10.3934/eect.2020075
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