Feshbach resonance: a one dimensional example

TL;DR

This paper presents a simple one-dimensional model demonstrating Feshbach resonance, involving a spin-1/2 particle with a delta potential and magnetic field, providing a clear example of the phenomenon.

Contribution

It introduces a solvable one-dimensional model illustrating Feshbach resonance with coupled channels and magnetic field tuning, offering insights into the phenomenon's fundamental mechanisms.

Findings

The model admits a closed-form solution.

Feshbach resonance occurs through magnetic field tuning.

The example clarifies the interaction of coupled channels.

Abstract

We present a simple one-dimensional example of a spin 1/2 particle submitted to a delta-type potential which interacs differently with the two components of the wavefunction and to an external magnetic field. It has two coupled channels, admits a closed solution and features the Feshbach resonance phenomenon by proper tunning of the magnetic field.