  We show that fixed energy scattering measurements for the magnetic
Schroedinger operator uniquely determine the magnetic field and electric
potential in dimensions $n \geq 3$. 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 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 Schroedinger equation via a pseudodifferential conjugation
argument.
