Quantization of the Nonlinear Schrodinger Equation on the Half Line

TL;DR

This paper introduces a new algebraic framework called boundary exchange algebra to solve the nonlinear Schrödinger equation on a half line with mixed boundary conditions, advancing the mathematical understanding of boundary effects in quantum systems.

Contribution

It develops the boundary exchange algebra as a novel structure to establish second quantized solutions for the nonlinear Schrödinger equation with boundaries.

Findings

Successful formulation of second quantized solutions on the half line

Introduction of boundary exchange algebra as a substitute for Zamolodchikov-Faddeev algebra

Enhanced mathematical tools for boundary quantum integrable systems

Abstract

We establish the second quantized solution of the nonlinear Schrodinger equation on the half line with a mixed boundary condition. The solution is based on a new algebraic structure, which we call boundary exchange algebra and which substitutes, in the presence of boundaries, the familiar Zamolodchikov-Faddeev algebra.