Stable determination of coefficients in the dynamical Schr\"odinger equation in a magnetic field

In this paper we consider the inverse problem of determining on a compact Riemannian manifold the electric potential or the magnetic field in a Schr"odinger equation with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the magnetic Schr"odinger equation. We prove that the knowledge of the Dirichlet-to-Neumann map for the Schr"odinger equation uniquely determines the magnetic field and the electric potential and we establish H"older-type stability.