An expression is obtained for the total mechanical energy ofa compressible homogenous sphere with allowance for pressure and rotation (Maclaurin spheroid). An exact solution is obtained for the Schroedinger equation describing the stationary states of a massive particle, a quanton, these being the states to which a self-gravitating body can pass when it undergoes collapse. Quanton division reactions are considered. For a sufficiently small value of the factor that renormalizes the gravitational constant, the quanton masses, which can be measured by their exterior gravitational field, lie in the mass range of cosmic bodies. In the decay process, quantons can be transformed into macroscopic bodies. The expressions obtained in the paper make it possible to calculate models of the formation of definite systems of objects observed in the universe.