  We consider non-relativistic point-particles coupled to Einstein gravity and
their canonical quantization. From the resulting Wheeler-DeWitt wave equation
we determine a quantum version of geometrodynamics, where the coupled evolution
of particle positions and 3-metric is guided by the wave function. We find that
this quantum dynamics implies a quantum extension of the Einstein equations.
The conserved energy-momentum tensor now contains a quantum contribution. This
conceptually-simple set up is promising both for deriving semiclassical and
weak field approximations to the quantum Einstein equations and is thus
important for the development of quantum corrections to computational general
relativity.
