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 Bilinear control of discrete spectrum Schrödinger operators
 The bilinear control problem of the Schrödinger equation $i\frac{\partial}{\partial t}\psi(t)$ $=( A+u(t) B)\psi(t)$, where $u(t)$ is the control function, is investigated through topological irreducibility of the set $\mathfrak{M}=\{ e^{-it (A+u B)}, u\in \mathbb{R}, t>0\}$ of bounded operators. Under an appropriate assumption on $B$, this allows to prove the approximate controllability of such systems when the uncontrolled Hamiltonian $A$ has a simple discrete spectrum.
 Keyword(s) : Bilinear control – Approximate controllability – Schrödinger operators – Invariant subspaces – Topological irreducibility
 hal-00479584, version 1 http://hal.archives-ouvertes.fr/hal-00479584 oai:hal.archives-ouvertes.fr:hal-00479584 From: Zied Ammari <> Submitted on: Friday, 30 April 2010 21:28:00 Updated on: Tuesday, 4 May 2010 09:21:43