This article is the fourteenth part of the scientific project under the general title "Geometrized Vacuum Physics Based on the Algebra of Signature" (GVPh&AS) [1,2,3,4,5,6,7,8,9, 10,11,12,13]. In this article, the stochastic metric-dynamic model (SMDM) of the "hydrogen atom" is considered, constructed on the basis of the principles and mathematical apparatus of GVPh&AS. A similar methodology can be applied to study the internal structure of all known "atoms" and "molecules" of both the picoscopic level of matter organization (~10^—11 — 10^—14cm), and other levels: microscopic, planetary, galactic, etc. A stochastic Schrödinger equation for the "hydrogen atom" with effective potentiality is proposed, which may allow for a refinement of the fine structure of the emission spectrum of this stable vacuum formation without the use of radiative corrections. A distinctive feature of the SMDM from the quantum mechanical approach (in the Copenhagen interpretation) is that the mathematics of the GVPh&AS allows for the creation of a visual simulation of intra-atomic processes in a form convenient for our perception, i.e., as if peering inside the "atom" and mentally observing the cosmic grandeur of the processes occurring there.