  An approach to the quantization of gravity in the presence matter is examined
which starts from the classical Einstein-Hilbert action and matter approximated
by "point" particles minimally coupled to the metric. Upon quantization, the
Hamilton constraint assumes the form of the Schr\"odinger equation: it contains
the usual Wheeler-DeWitt term and the term with the time derivative of the wave
function. In addition, the wave function also satisfies the Klein-Gordon
equation, which arises as the quantum counterpart of the constraint among
particles' momenta. Comparison of the novel approach with the usual one in
which matter is represented by scalar fields is performed, and shown that those
approaches do not exclude, but complement each other. In final discussion it is
pointed out that the classical matter could consist of superparticles or
spinning particles, described by the commuting and anticommuting Grassmann
coordinates, in which case spinor fields would occur after quantization.
