Gauge equivalence and inverse scattering for long-range magnetic potentials

For Schroedinger operators with long-range magnetic vector potentials and short-range electric scalar potentials in an exterior domain $Ω$ in ${\bf R}^n$ with $n \geq 2$, we show that there is a one-to-one correspondence between the gauge equivalent classes of Hamiltonians and those of S-matrices if $Ω$ is exterior to a bounded convex obstacle.

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