Quantization of the Derivative Nonlinear Schrodinger Equation

TL;DR

This paper explores the quantum version of the derivative nonlinear Schrödinger equation, revealing exact solvability of the N-body problem, and offering new insights into classical features like solitons through quantization.

Contribution

It introduces an exact quantum solution for the derivative nonlinear Schrödinger equation, connecting quantum mechanics with classical integrable structures.

Findings

N-body quantum problem is exactly solvable

Existence of bound states with particle number limit

Quantum analysis elucidates classical soliton behavior

Abstract

We study the quantum mechanics of the derivative nonlinear Schrodinger equation which has appeared in many areas of physics and is known to be classically integrable. We find that the N-body quantum problem is exactly solvable with both bound states (with an upper bound on the particle number) and scattering states. Quantization provides an alternative way to understand various features of the classical model, such as chiral solitons and two-soliton scattering.