Discrete States of Continuous Electrically Charged Matter

By introducing in the Euler equation non mechanical (mesic) force densities equal to the products of corresponding potentials and gradient of the matter density, and supposing that the dynamical process has a diffusion character, the equation of continuity with internal sources (both positive and negative) is obtained. These sources are proportional to the algebraic sum of electrostatic, kinetic and proper energy densities, the constant of proportionality being the inverse value of the diffusion constant D = ℎ/2m, taken with negative sign. The stationary state is obtained if the solution of the continuity equation holds in any point of the object, which is possible only for discrete values of the constant E with dimension of energy, entering in the equation of continuity. The equation of continuity can be transformed to the Bohm equation with the quantum potential, which may be solved by reducing it to the corresponding Schroedinger equation. Thus the spatial distribution of the density of matter is given by the square of the Schroedinger wave function. Once the density distribution function is known, the velocity u(vector) in the diffusion process can be calculated and the process is deterministic. Superimposed to the diffusion process is the classical motion with velocity v(vector), for which the equation of continuity without internal sources of matter holds. (author)