  In this paper we investigate the inverse problem of determining the time
independent scalar potential of the dynamic Schr\"odinger equation in an
infinite cylindrical domain, from partial measurement of the solution on the
boundary. Namely, if the potential is known in a neighborhood of the boundary
of the spatial domain, we prove that it can be logarithmic stably determined in
the whole waveguide from a single observation of the solution on any arbitrary
strip-shaped subset of the boundary.
