Structure of the Semi-Classical Amplitude for General Scattering Relations

DOI10.1080/03605300500299588zbMath1088.81091arXivmath/0407502OpenAlexW2053898254MaRDI QIDQ5713469

Ivana Alexandrova

Publication date: 14 December 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0407502

zbMATH Keywords

Semi-classical analysisScattering AmplitudeScattering relation

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) (2)-body potential quantum scattering theory (81U05) Pseudodifferential operators and other generalizations of partial differential operators (35S99)

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Cites Work

• Asymptotic behavior of scattering amplitudes in semi-classical and low energy limits
• Sur la rigidite imposee par la longueur des geodesiques
• A problem of reconstructing a Riemannian metric
• Sojourn times and asymptotic properties of the scattering matrix
• Semiclassical estimates in asymptotically Euclidean scattering
• High frequency asymptotics for the scattering matrix and the inverse problem of acoustical scattering
• Complex Scaling and the Distribution of Scattering Poles
• Semi-Classical Behavior of the Scattering Amplitude for Trapping Perturbations at Fixed Energy
• Semi-classical estimates on the scattering determinant
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