Inverse scattering for the magnetic Schroedinger operator

Details Inverse scattering for the magnetic Schroedinger operator Inverse scattering for the magnetic Schroedinger operator

2009-08-27

arxiv.org/abs/0908.3977v1

Mathematics

Analysis of PDEs

23 pages

Scientific paper

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.

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