Exact controllability of the Schrödinger equation

摘要

In this paper we study the controllability of the linear Schrödinger equation on bounded domains in Rn. First we state and prove a simple functional analytic characterization of the exact controllability of abstract Schrödinger type equations which does not use the Hilbert uniqueness method. In a second part, we discuss generalizations of results of Machtyngier [SIAM J. Control Optim. 32 (1994) 24] on the exact internal and boundary controllability of Schrödinger equation by allowing lower order terms in the Schrödinger equation; this may be a first step to prove results on the exact controllability of (semilinear) nonlinear Schrödinger equations (which is a big problem).