Wave mechanics for gravity with point-particles

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 evolution particle positions 3-metric is guided by function. find that this dynamics implies extension equations. The conserved energy-momentum tensor now contains contribution. This conceptually-simple set up promising both for deriving semiclassical weak field approximations equations thus important development corrections computational general relativity.