Remarks on the controllability of the Schrödinger equation

Abstract

In this paper we present some results on the controllability of the Schrodinger equation. We first discuss the controllability of the linear equation with a control distributed along a subdomain or subset of the boundary of the domain where the equation holds. We also analyze some possible extensions to semilinear equations in which the nonlinearity involves the state equation but the control enters linearly in the system. Finally we study the model bilinear control problem arising in Quantum Chemistry and some issues related with the numerical approximation of the controls.