Mesic forces in quantum mechanics

Abstract

Relativistic equations were derived of the motion of a continuous, electrically and mesically charged substance obeying the simple diffusion law and moving in a constant external electrical scalar potential. The relevant equation of continuity is presupposed with the right side different from zero, corresponding to the internal sources of matter. It is shown that if the matter distribution satisfies this equation of continuity, the gradient of the external potential is just compensated by the inner potential gradient of the electrically charged matter. In this case, the acceleration of the substance is zero and all dynamical variables are time independent. Thus, the validity of the equation of continuity has to be considered as a necessary and sufficient condition for the existence of steady, time independent distribution of the continuous substance density. Our considerations are limited to continua with spins equal zero because the osmotic velocity satisfies the simple diffusion law. The simplest way to find a solution of the nonlinear equation of continuity is its linearization, leading directly to the Schrödinger equation for steady bound states, from which the eigenvalues can be obtained. Substituting the latter into the nonlinear equation of continuity, one can reveal its solution.