Observability and Control of Schrödinger Equations

We propose an exact controllability result for Schrödinger equations in bounded domains under the Bardos--Lebeau--Rauch geometric control condition with an estimate of the control which is explicit with respect to the time of controllability. Also, we prove an explicit in time logarithmic observability estimate for the Schrödinger equation, where no geometrical conditions are supposed on the domain.