Semiclassical scattering amplitude at the maximum point of the potential

Details Semiclassical scattering amplitude at the maximum point of the potential Semiclassical scattering amplitude at the maximum point of the potential

2007-04-12

arxiv.org/abs/0704.1632v2

Mathematics

Analysis of PDEs

62 pages, 2 figures

Scientific paper

We compute the scattering amplitude for Schr\"odinger operators at a critical energy level, corresponding to the maximum point of the potential. We follow the wrok of Robert and Tamura, '89, using Isozaki and Kitada's representation formula for the scattering amplitude, together with results from Bony, Fujiie, Ramond and Zerzeri '06 in order to analyze the contribution of trapped trajectories.

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