  The most general two-dimensional dilaton gravity theory coupled to an Abelian
gauge field is considered. It is shown that, up to spacetime diffeomorphisms
and $U(1)$ gauge transformations, the field equations admit a two-parameter
family of distinct, static solutions.
  For theories with black hole solutions, coordinate invariant expressions are
found for the energy, charge, surface gravity, Hawking temperature and entropy
of the black holes. The Hawking temperature is proportional to the surface
gravity as expected, and both vanish in the case of extremal black holes in the
generic theory. A Hamiltonian analysis of the general theory is performed, and
a complete set of (global) Dirac physical observables is obtained. The theory
is then quantized using the Dirac method in the WKB approximation. A connection
between the black hole entropy and the imaginary part of the WKB phase of the
Dirac quantum wave functional is found for arbitrary values of the mass and
$U(1)$ charge. The imaginary part of the phase vanishes for extremal black
holes and for eternal, non-extremal Reissner-Nordstrom black holes.
