Inverse scattering for the magnetic Schrödinger operator

We show that fixed energy scattering measurements for the magnetic Schrödinger operator uniquely determine the magnetic field and electric potential in dimensions n?3. The magnetic potential, its first derivatives, and the electric potential are assumed to be exponentially decaying. This improves an earlier result of Eskin and Ralston (1995) [5] which considered potentials with many derivatives. The proof is close to arguments in inverse boundary problems, and is based on constructing complex geometrical optics solutions to the Schrödinger equation via a pseudodifferential conjugation argument.