  We study a manifestly unitary formulation of 2d dilaton quantum gravity based
on the reduced phase space quantization. The spacetime metric can be expanded
in a formal power series of the matter energy-momentum tensor operator. This
expansion can be used for calculating the quantum corrections to the classical
black hole metric by evaluating the expectation value of the metric operator in
an appropriate class of the physical states. When the normal ordering in the
metric operator is chosen to be with respect to Kruskal vacuum, the lowest
order semiclassical metric is exactly the one-loop effective action metric
discovered by Bose, Parker and Peleg. The corresponding semiclassical geometry
describes an evaporating black hole which ends up as a remnant. The calculation
of higher order corrections and implications for the black hole fate are
discussed.
