Uniqueness of the solution of the Gaudin's equations, which describe a one-dimensional system of point bosons with zero boundary conditions

TL;DR

This paper proves that the Gaudin's equations for a one-dimensional system of spinless point bosons with zero boundary conditions have a unique real solution for each set of quantum numbers, ensuring well-defined energy states.

Contribution

It establishes the uniqueness of solutions to Gaudin's equations for this specific quantum system, clarifying the mathematical structure of the model.

Findings

Gaudin's equations have a unique real solution for each quantum number set.

The result applies to a system of spinless point bosons with zero boundary conditions.

Ensures well-defined energy states in the model.

Abstract

We show that the system of Gaudin's equations for quasimomenta k_{j}, which describes a one-dimensional system of spinless point bosons with zero boundary conditions, has the unique real solution for each set of quantum numbers n_{j}.