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We derive conditional stability estimates for inverse scattering problemsrelated to time harmonic magnetic Schr\"odinger equation. We prove logarithmictype estimates for retrieving the magnetic (up to a gradient) and electricpotentials from near field or far field maps. Our approach combines techniquesfrom similar results obtained in the literature for inhomogeneous inversescattering problems based on the use of geometrical optics solutions.

Stability estimate for an inverse problem for the time harmonic magnetic Schr\"odinger operator from the near and far field pattern