Inverse Scattering at Fixed Energy for Radial Magnetic Schrodinger Operators with Obstacle in Dimension Two

We study an inverse scattering problem at fixed energy for radial magnetic Schr odinger operators on R2\ B(0, r0), where r0 is a positive and arbitrarily small radius. We assume that the magnetic potential A satisfies a gauge condition, and we consider the class C of smooth, radial and compactly supported electric potentials and magnetic fields denoted by V and B, respectively. If (V, B) and (V, B) are two couples belonging to C, we then show that if the corresponding phase shifts dl and dl (i. e., the scattering data at fixed energy) coincide for all l. L, where L. N satisfies the Muntz condition l. L 1 l = +8, then V (x) = V (x) and B(x) = B (x) outside the obstacle B(0, r0). The proof uses the complex angular momentum method and is close in spirit to the celebrated Borg-Marchenko uniqueness theorem.