Global exact controllability in infinite time of Schrödinger equation: multidimensional case

Details Global exact controllability in infinite time of Schrödinger equation: multidimensional case Global exact controllability in infinite time of Schrödinger equation: multidimensional case

2012-01-17

arxiv.org/abs/1201.3445v1

Mathematics

Analysis of PDEs

Scientific paper

We prove that the multidimensional Schr\"odinger equation is exactly controllable in infinite time near any point which is a finite linear combination of eigenfunctions of the Schr\"odinger operator. We prove that, generically with respect to the potential, the linearized system is controllable in infinite time. Applying the inverse mapping theorem, we prove the controllability of the nonlinear system.

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