A note on the Schr\"odinger operator with a long-range potential
Spectral Theory
2018-10-09 v1 Mathematical Physics
Classical Analysis and ODEs
Functional Analysis
math.MP
Abstract
Our goal is to develop spectral and scattering theories for the one-dimensional Schr\"odinger operator with a long-range potential , . Traditionally, this problem is studied with a help of the Green-Liouville approximation. This requires conditions on the first two derivatives and . We suggest a new Ansatz that allows us to develop a consistent theory under the only assumption .
Cite
@article{arxiv.1810.03112,
title = {A note on the Schr\"odinger operator with a long-range potential},
author = {D. R. Yafaev},
journal= {arXiv preprint arXiv:1810.03112},
year = {2018}
}