Many authors have attempted to derive the fundamental equations of quantum mechanics from classical hydrodynamics. In the present contribution we presume that the continuous, electrically charged material substance moves simultaneously under the influence of the electric field and at the same time undergoes a diffusion process. This assumption leads to the appearance of non-mechanical (mezic) type forces responsible for inner sources of matter (positive or negative), similar to those whose existence is supposed to exist in relativistic hydrodynamics. We obtained a non-linear differential equation, convertible by linearization to a form coinciding with the Schrödinger equation, as a condition for the establishment of the same steady states with discrete energies.