Bilinear control of discrete spectrum Schrödinger operators

Abstract

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 $\mathfrak{M}=\{e^{-it(A+uB)},u\in \mathbb{R},t>0\}$ of bounded operators. This allows to prove the approximate controllability of such systems when the uncontrolled Hamiltonian $A$ has a simple discrete spectrum and under an appropriate assumption on $B$.

This paper has been withdrawn by the authors due to a crucial gap in the proof of the main theorem.

References in corpus (1)

• Controllability of the discrete-spectrum Schrodinger equation driven by an external field