  We clarify some issues related to the evaluation of the mean value of the
energy-momentum tensor for quantum scalar fields coupled to the dilaton field
in two-dimensional gravity. Because of this coupling, the energy-momentum
tensor for the matter is not conserved and therefore it is not determined by
the trace anomaly. We discuss different approximations for the calculation of
the energy-momentum tensor and show how to obtain the correct amount of Hawking
radiation. We also compute cosmological particle creation and quantum
corrections to the Newtonian potential.
