Semiclassical asymptotics for the scattering amplitude in the presence of focal points at infinity

We consider scattering in \Rⁿ, $n\ge 2$, described by the Schr\"odinger operator P(h)=-h²\Delta+V, where $V$ is a short-range potential. With the aid of Maslov theory, we give a geometrical formula for the semiclassical asymptotics as $h\to 0$ of the scattering amplitude f(ω_-,ω₊;\lambda,h) ω₊\neqω_-) which remains valid in the presence of focal points at infinity (caustics). Crucial for this analysis are precise estimates on the asymptotics of the classical phase trajectories and the relationship between caustics in euclidean phase space and caustics at infinity.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Potsdam

Year

2006

Author dc:creator

• Hohberger, Horst

Contributors dc:contributor

• Klein, Markus

• Semiklassik
• mathematics
• physics
• scattering theory
• semiclassics
• scattering amplitude

Repository record source_url

https://publishup.uni-potsdam.de/frontdoor/index/index/docId/1093

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-potsdam:1093