Poor man's derivation of the Bethe-Ansatz equations for the Dicke model

TL;DR

This paper provides an accessible derivation of the Bethe-Ansatz equations for the Dicke model, simplifying the understanding of its exact solutions through basic algebraic relations.

Contribution

It introduces a straightforward derivation method for the Bethe-Ansatz equations of the Dicke model using only fundamental commutation relations and an informed eigenstate Ansatz.

Findings

Derivation of Bethe-Ansatz equations for the Dicke model

Simplified approach using basic commutation relations

Enhanced understanding of the model's exact solutions

Abstract

We present an elementary derivation of the exact solution (Bethe-Ansatz equations) of the Dicke model, using only commutation relations and an informed Ansatz for the structure of its eigenstates.