Geometric Scattering for Schr\"odinger Operators with Asymptotically Homogeneous Potentials of Order Zero

TL;DR

This paper studies Schrödinger operators with order-zero potentials on asymptotically conic manifolds, establishing the existence and completeness of wave operators relative to a natural free Hamiltonian.

Contribution

It proves the existence and completeness of wave operators for Schrödinger operators with order-zero potentials on asymptotically conic manifolds, extending scattering theory in this setting.

Findings

Wave operators exist for the considered Schrödinger operators.

Wave operators are complete, capturing the full scattering behavior.

Results apply to potentials of order zero on asymptotically conic manifolds.

Abstract

In this paper we consider Schr\"oodinger operators with potentials of order zero on asymptotically conic manifolds. We prove the existence and the completeness of the wave operators with a naturally defined free Hamiltonian.