This article is the thirteenth part of the scientific project under the general title "Geometrized Vacuum Physics Based on the Algebra of Signature " [1,2,3,4,5,6,7,8,9,10,11,12]. This article is aimed at substantiating the assertion that there is no difference in the mathematical description of the behavior of objects in the macrocosm and the microcosm. The hierarchical cosmological model proposed in the previous articles of this project assumes that the metric-dynamic models of all "corpuscles", regardless of their size (for example, "elementary particles", naked "planets" and "stars", as well as naked "galaxies") are structured almost identically. The main differences between them are associated primarily with the distinguishability of small details. The larger the "corpuscle", the more subtly its infrastructure is manifested. However, the similarity of "corpuscles" of different sizes is not limited to the coincidence of their shape. Their random movements (i.e., chaotic deviations of the core of the "corpuscles" from their mean positions) also obey the same laws. The article presents the derivation of the stochastic Schrödinger equations and self-diffusion equation, suitable for describing the averaged (including quantized) states of stochastic systems of any scale. It is shown that, for example, the chaotically shifting core of a planet (or star) can have a quantum set of possible averaged states, similar to the excited states of an electron in an atom. It is suggested that when the core of a planet (or star) transitions from one quantum state to another, the interior of this celestial body can absorb or emit gravitational waves. This hypothesis may form the basis of stellar-planetary gravitational spectroscopy.