Controllability of Schrödinger equations
Séminaire Équations aux dérivées partielles (Polytechnique) (2005-2006), Talk no. 9, 18 p.

One considers a quantum particle in a 1D moving infinite square potential well. It is a nonlinear control system in which the state is the wave function of the particle and the control is the acceleration of the potential well. One proves the local controllability around any eigenstate, and the steady state controllability (controllability between eigenstates) of this control system. In particular, the wave function can be moved from one eigenstate to another one, exactly and in finite time, by moving the potential well in a suitable way.

The proof uses moment theory, a Nash-Moser theorem, Coron’s return method and expansions to the second order.

This article summarizes two works : [4] and a joint work with Jean-Michel Coron [5].

@article{SEDP_2005-2006____A9_0,
author = {Beauchard, Karine},
title = {Controllability of Schr\"odinger equations},
journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2005-2006},
note = {talk:9},
mrnumber = {2276075},
language = {en},
url = {http://www.numdam.org/item/SEDP_2005-2006____A9_0}
}

Beauchard, Karine. Controllability of Schrödinger equations. Séminaire Équations aux dérivées partielles (Polytechnique) (2005-2006), Talk no. 9, 18 p. http://www.numdam.org/item/SEDP_2005-2006____A9_0/

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