We establish the second quantized solution of the nonlinear Schrodinge
r equation on the half line with a mixed boundary condition. The solut
ion is based on a new algebraic structure, which we call boundary exch
ange algebra and which substitutes, in the presence of boundaries, the
familiar Zamolodchikov-Faddeev algebra. (C) 1998 Elsevier Science B.V
. All rights reserved.