# Semi-classical resolvent estimates for short-range l $\infty$ potentials. II

## TL;DR

This paper establishes semi-classical resolvent estimates for certain real-valued, short-range and long-range potentials in higher dimensions, advancing understanding of spectral properties in quantum mechanics.

## Contribution

It provides new resolvent estimates for potentials composed of long-range and short-range parts, extending previous results to broader classes of potentials.

## Key findings

- Proves resolvent estimates for potentials V = VL + VS with specified decay.
- Handles potentials with both long-range and short-range components.
- Extends semi-classical analysis to more general potential classes.

## Abstract

We prove semi-classical resolvent estimates for real-valued potentials V $\in$ L $\infty$ (R n), n $\ge$ 3, of the form V = VL + VS, where VL is a long-range potential which is C 1 with respect to the radial variable, while VS is a short-range potential satisfying VS(x) = O x --$\delta$ with $\delta$ > 1.