Semiclassical scattering amplitude at the maximum point of the potential

Ivana Alexandrova (1) , Jean-Francois Bony (2) , Thierry Ramond (3)

1 Department of Mathematics
2 IMB - Institut de Mathématiques de Bordeaux
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]; Analyse fonctionnelle [math.FA]; Théorie spectrale [math.SP]

Ivana Alexandrova, Jean-Francois Bony, Thierry Ramond. Semiclassical scattering amplitude at the maximum point of the potential. Asymptotic Analysis, 2008, 58 (1-2), pp.57-125. ⟨hal-00281584⟩