  The nonlinear Schrodinger equation on the half line with mixed boundary
condition is investigated. After a brief introduction to the corresponding
classical boundary value problem, the exact second quantized solution of the
system is constructed. The construction is based on a new algebraic structure,
which is called in what follows boundary algebra and which substitutes, in the
presence of boundaries, the familiar Zamolodchikov-Faddeev algebra. The
fundamental quantum field theory properties of the solution are established and
discussed in detail. The relative scattering operator is derived in the
Haag-Ruelle framework, suitably generalized to the case of broken translation
invariance in space.
