  We present a generalization of the boundary state formalism for the bosonic
string that allows us to calculate the overlap of the boundary state with
arbitrary closed string states. We show that this generalization exactly
reproduces world-sheet sigma model calculations, thus giving the correct
overlap with both on- and off-shell string states, and that this new boundary
state automatically satisfies the requirement for integrated vertex operators
in the case of non-conformally invariant boundary interactions.
