The Nonlinear Schrodinger Equation on the Half Line

摘要

The nonlinear Schrodinger equation on the half line with mixed boundarycondition is investigated. After a brief introduction to the correspondingclassical boundary value problem, the exact second quantized solution of thesystem is constructed. The construction is based on a new algebraic structure,which is called in what follows boundary algebra and which substitutes, in thepresence of boundaries, the familiar Zamolodchikov-Faddeev algebra. Thefundamental quantum field theory properties of the solution are established anddiscussed in detail. The relative scattering operator is derived in theHaag-Ruelle framework, suitably generalized to the case of broken translationinvariance in space.