# Quasimomentum of an elementary excitation for a system of point bosons under zero boundary conditions

## TL;DR

This paper derives the formula for quasimomentum of elementary excitations in a one-dimensional system of point bosons with zero boundary conditions, showing that their dispersion laws match those with periodic boundaries.

## Contribution

It provides the first explicit formula for quasimomentum under zero boundary conditions using Bethe ansatz solutions.

## Key findings

- Quasimomentum formula for elementary excitations under zero BCs
- Dispersion laws match those with periodic BCs
- Validates Bethe ansatz approach for boundary conditions

## Abstract

As is known, an elementary excitation of a many-particle system with boundaries is not characterized by a definite momentum. We obtain the formula for the quasimomentum of an elementary excitation for a one-dimensional system of $N$ spinless point bosons under zero boundary conditions (BCs). In this case, we use the Gaudin's solutions obtained with the help of the Bethe ansatz. We have also found the dispersion laws of the particle-like and hole-like excitations under zero BCs. They coincide with the known dispersion laws obtained for periodic BCs.