  In classical two-dimensional pure dilaton gravity, and in particular in
spherically symmetric pure gravity in d dimensions, the generalized Birkhoff
theorem states that, for a suitable choice of coordinates, the metric
coefficients are only functions of a single coordinate. It is interesting to
see how this result is recovered in quantum theory by the explicit construction
of the Hilbert space. We examine the CGHS model, enforce the set of auxiliary
conditions that select physical states a` la Gupta-Bleuler, and prove that the
matrix elements of the metric and of the dilaton field obey the classical
requirement. We introduce the mass operator and show that its eigenvalue is the
only gauge invariant label of states. Thus the Hilbert space is equivalent to
that obtained by quantum mechanical treatment of the static case. This is the
quantum form of the Birkhoff theorem for this model.
