  Boundary conditions changing operators have played an important role in
conformal field theory. Here, we study their equivalent in the case where a
mass scale is introduced, in an integrable way, either in the bulk or at the
boundary. More precisely, we propose an axiomatic approach to determine the
general scalar products ${}_b<\theta_1, ... ,\theta_m||\theta'_1, ...
,\theta'_{n}>_a$ between asymptotic states in the Hilbert spaces with $a$ and
$b$ boundary conditions respectively, and compute these scalar products
explicitely in the case of the Ising and sinh-Gordon models with a mass and a
boundary interaction. These quantities can be used to study statistical systems
with inhomogeneous boundary conditions, and, more interestingly maybe,
dynamical problems in quantum impurity problems. As an example, we obtain a
series of new exact results for the transition probability in the double well
problem of dissipative quantum mechanics.
