Exact controllability of the Schrodinger equation

In this paper we study the controllability of the linear Schrodinger equation on bounded domains in R-n. First we state and prove a simple functional analytic characterization of the exact controllability of abstract Schrodinger 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 Schrodinger equation by allowing lower order terms in the Schrodinger equation; this may be a first step to prove results on the exact controllability of (semilinear) nonlinear Schrodinger equations (which is a big problem). (C) 2002 Elsevier Science Inc. All rights reserved.