Generic controllability properties for the bilinear Schroedinger equation
In a recent paper we proposed a set of necessary conditions for the
approximate controllability of a discrete-spectrum bilinear
Schroedinger equation on a fixed domain. These conditions are expressed in terms of the controlled potential and of the eigenpairs of the uncontrolled Schroedinger operator. The aim of this presentation is to show that these conditions are generic with respect to the uncontrolled or the controlled potential.
The results are obtained by analytic perturbation arguments and
through the study of asymptotic properties of eigenfunctions.