# A Quantum Model of Feshbach Resonances

## TL;DR

This paper develops a quantum two-channel scattering model to analyze Feshbach resonances, providing rigorous resonance counting, localization, and an expansion of the scattering length near resonances in both perturbative and non-perturbative regimes.

## Contribution

It introduces a detailed mathematical framework for analyzing Feshbach resonances, including resonance counting, localization, and effective scattering length expansion.

## Key findings

- Resonance counting and localization in perturbative and non-perturbative regimes
- Expansion of the effective scattering length near resonances
- Rigorous analysis of energy-dependent effective potentials

## Abstract

We consider a quantum model of two-channel scattering to describe the mechanism of a Feshbach resonance. We perform a rigorous analysis in order to count and localize the energy resonances in the perturbative regime, i.e., for small inter-channel coupling, and in the non-perturbative one. We provide an expansion of the effective scattering length near the resonances, via a detailed study of an effective Lippmann-Schwinger equation with energy-dependent potential.

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Source: https://tomesphere.com/paper/1901.08282