New Formula for the Eigenvectors of the Gaudin Model in the sl(3) Case

TL;DR

This paper introduces explicit formulas for eigenvectors of the Gaudin model in the sl(3) case, utilizing a novel operator P and Bethe Ansatz equations to derive eigenvalues.

Contribution

It provides a new explicit construction of eigenvectors for the Gaudin model in the sl(3) case, advancing the understanding of its spectral properties.

Findings

Derived explicit eigenvector formulas using operator P

Connected eigenvalues to Bethe Ansatz equations

Enhanced analytical tools for the Gaudin model in sl(3)

Abstract

We propose new formulas for eigenvectors of the Gaudin model in the $\sl(3)$ case. The central point of the construction is the explicit form of some operator P, which is used for derivation of eigenvalues given by the formula $| w_1, w_2) = \sum_{n=0}^\infty P^n/n! | w_1, w_2,0>$, where $w_1$, $w_2$ fulfil the standard well-know Bethe Ansatz equations.