Minimal velocity bound for Schroedinger-type operator with fractional powers
Mathematical Physics
2025-01-07 v5 math.MP
Abstract
It is known in scattering theory that the minimal velocity bound plays a conclusive role in proving the asymptotic completeness of the wave operators. In this study, we prove the minimal velocity bound and other important estimates for the two-body Schroedinger-type operator with fractional powers. We assume that the pairwise potential functions belong to broad classes that include long-range decay and Coulomb-type local singularities. Our estimates are expected to be applied to prove the asymptotic completeness for the fractional Schroedinger-type operators in various (not only short-range but also long-range and N-body) situations.
Keywords
Cite
@article{arxiv.2007.05388,
title = {Minimal velocity bound for Schroedinger-type operator with fractional powers},
author = {Atsuhide Ishida},
journal= {arXiv preprint arXiv:2007.05388},
year = {2025}
}