A Carleman estimate for infinite cylindrical quantum domains and the application to inverse problems

We consider the inverse problem of determining the time-independent scalar potential q of the dynamic Schrodinger equation in an infinite cylindrical domain Omega, from one Neumann boundary observation of the solution. Assuming that q is known outside some fixed compact subset of Omega, we prove that q may be Lipschitz stably retrieved by choosing the Dirichlet boundary condition of the system suitably. Since the proof is by means of a global Carleman estimate designed specifically for the Schrodinger operator acting in an unbounded cylindrical domain, the measurement of the Neumann data is performed on an infinitely extended subboundary of the cylinder.