Determining Asymptotics of Magnetic Fields from Fixed Energy Scattering Data

The problem of recovering the asymptotics of a short range perturbation of the Euclidean Laplacian on n dimensional Eudlidean space from fixed energy scattering data is studied. It is shown that for greater than or equal to three that a magnetic potential is determined, modulo Gauge invariance, by its scattering matrix at a fixed non-zero energy. This result also holds for a wide class of scattering manifolds.