Scattering for Schrödinger operators with conical decay

Abstract

We study the scattering properties of Schrödinger operators with potentials that have short-range decay along a collection of rays in ${\mathbb{R}}^d$. This generalizes the classical setting of short-range scattering in which the potential is assumed to decay along \emph{all} rays. For these operators, we show that any state decomposes into an asymptotically free piece and a piece which may interact with the potential for long times. We give a microlocal characterization of the scattering states in terms of the dynamics and a corresponding description of their complement. We also show that in certain cases these characterizations can be purely spatial.

References in corpus (2)

• Spectral properties of soft quantum waveguides
• Scattering for Schrödinger operators with potentials concentrated near a subspace