  We show that the ``boundary crossing-unitarity equation" recently proposed by
Ghoshal and Zamolodchikov is a consequence of the boundary bootstrap equation
for the S-matrix and the wall-bootstrap equation. We solve this set of
equations for all affine Toda theories related to simply laced Lie algebras,
obtaining explicit formulas for the W-matrix which encodes the scattering of a
particle with the boundary in the ground state. For each theory there are two
solutions to these equations, related by CDD-ambiguities, each giving rise to
different kind of physics.
