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

An inverse stability result for non compactly supported potentials by one arbitrary lateral Neumann observation