Semiclassical scattering amplitude at the maximum point of the potential

2007/04/12 by Alexandrova, Ivana, Bony, Jean-Francois, Ramond, Thierry
#35B38 #35C20 #35P25 #81U20 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.0704.1632

Abstract

We compute the scattering amplitude for Schrödinger 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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