Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time

Details Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time

2003-09-17

arxiv.org/abs/math-ph/0309043v2

Inverse Problems vol. 20 (2004) 893-917

Physics

Mathematical Physics

In this revised version I give a more detailed motivation of the class of potentials that I consider and I have corrected some

Scientific paper

10.1088/0266-5611/20/3/015

We prove that the scattering matrix at a fixed quasi--energy determines uniquely a time--periodic potential that decays exponentially at infinity. We consider potentials that for each fixed time belong to $L^{3/2}$ in space. The exponent 3/2 is critical for the singularities of the potential in space. For this singular class of potentials the result is new even in the time--independent case, where it was only known for bounded exponentially decreasing potentials.

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