  Correlation functions and form factors in vertex models or spin chains are
known to satisfy certain difference equations called the quantum
Knizhnik-Zamolodchikov equations. We find similar difference equations for the
case of semi-infinite spin chain systems with integrable boundary conditions.
We derive these equations using the properties of the vertex operators and the
boundary vacuum state, or alternatively through corner transfer matrix
arguments for the 8-vertex model with a boundary. The spontaneous boundary
magnetization is found by solving such difference equations. The boundary
$S$-matrix is also proposed and compared, in the sine-Gordon limit, with
Ghoshal--Zamolodchikov's result. The axioms satisfied by the form factors in
the boundary theory are formulated.
