  We investigate Hawking radiation from two-dimensional dilatonic black holes
using standard quantization techniques. In the background of a collapsing black
hole solution the Bogoliubov coefficients can be exactly determined. In the
regime after the black hole has settled down to an `equilibrium' state but
before the backreaction becomes important these give the known result of a
thermal distribution of Hawking radiation at temperature lambda/(2pi). The
density matrix is computed in this regime and shown to be purely thermal.
Similar techniques can be used to derive the stress tensor. The resulting
expression agrees with the derivation based on the conformal anomaly and can be
used to incorporate the backreaction. Corrections to the thermal density matrix
are also examined, and it is argued that to leading order in perturbation
theory the effect of the backreaction is to modify the Bogoliubov
transformation, but not in a way that restores information lost to the black
holes.
