The matter-energy intensity distribution in a quantum gravitational   system
  In the framework of the method of constraint system quantization, a quantum gravitational system (QGS) with the maximally symmetric geometry is studied. The state vector of the QGS satisfies the set of wave equations which describes the time evolution of a quantum system in the space of quantum fields. It is shown that this state vector can be normalized to unity. The generalization of the wave equations to the domain of negative values of the cosmic scale factor is made. For the arrow of time from past to future, the state vector describes the QGS contracting for the negative values of the scale factor and expanding for its positive values. The intensity distributions of matter are calculated for two exactly solvable models of spatially closed and flat QGSs formed by dust and radiation. The analogies with the motion in time of minimum wave packet for spatially closed QGS and with the phenomenon of diffraction in optics for flat QGS are drawn. 
V. E. Kuzmichev, V. V. Kuzmichev (Bogolyubov Institute for Theoretical   Physics)
gr-qc quant-ph