Regularity of a Schrödinger equation with Dirichlet control and colocated observation

This paper studies the basic properties of the Schrödinger equation defined on a bounded domain of Rn,n⩾2 with partial Dirichlet control and colocated observation. It is shown that the system is not only wellposed in the sense of D. Salamon but also regular in the sense of G. Weiss. It is also shown that the corresponding feedthrough operator is zero.