Resolvent and scattering matrix at the maximum of the potential

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We study the microlocal structure of the resolvent of the semi-classical Schrodinger operator with short range potential at an energy which is a unique non-degenerate global maximum of the potential. We prove that it is a semi-classical Fourier integral operator quantizing the incoming and outgoing Lagrangian submanifolds associated to the fixed hyperbolic point. We then discuss two applications of this result to describing the structure of the spectral function and the scattering matrix of the Schrodinger operator at the critical energy.
31 pages, 3 figures

Keywords

Analysis of PDEs, Mathematical Physics, 35P25;81U20;35S30;47A10;35B38

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/141544

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0711.0879
 http://arxiv.org/abs/0711.0879

Collections

arXiv