Quantization of the Derivative Nonlinear Schrodinger Equation

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.

11 pages, LaTeX. I have learnt that similar work has been published earlier, see Refs. 13-14