# Semiclassical Estimates for Scattering on the Real Line

## TL;DR

This paper establishes explicit semiclassical resolvent estimates for integrable potentials on the real line, utilizing the spherical energies method, with the novelty of weaker assumptions on the potential compared to previous higher-dimensional results.

## Contribution

It applies the spherical energies method to derive resolvent estimates under weaker potential assumptions on the real line.

## Key findings

- Explicit semiclassical resolvent estimates proved
- Method applicable with weaker potential assumptions
- Simpler proof compared to higher-dimensional cases

## Abstract

We prove explicit semiclassical resolvent estimates for an integrable potential on the real line. The proof is a comparatively easy case of the spherical energies method, which has been used to prove similar theorems in higher dimensions and in more complicated geometric situations. The novelty in our results lies in the weakness of the assumptions on the potential.