Time dependent quantum scattering theory on complete manifolds with a corner of codimension 2
Differential Geometry
2015-09-24 v2 Spectral Theory
Abstract
We show the existence and orthogonality of wave operators naturally associated to a compatible Laplacian on a complete manifold with a corner of codimension 2. In fact, we prove asymptotic completeness i.e. that the image of these wave operators is equal to the space of absolutely continuous states of the compatible Laplacian. We achieve this last result using time dependent methods coming from many-body Schr\"odinger equations.
Keywords
Cite
@article{arxiv.1210.5548,
title = {Time dependent quantum scattering theory on complete manifolds with a corner of codimension 2},
author = {Leonardo A. Cano García},
journal= {arXiv preprint arXiv:1210.5548},
year = {2015}
}
Comments
We prove asymptotic completeness for compatible Laplacians on complete manifolds with corners of codimension 2. This version adds references and corrects typos. appears in Rev.colomb.mat. vol.49 no.1 Bogot\'a jan./jun. 2015