Inference of Schr\"odinger's Equation from Classical-Mechanical Solution
  We set up the classical wave equation for a particle formed of an oscillatory zero-rest-mass charge together with its resulting electromagnetic waves, traveling in a potential field $V$ in a susceptible vacuum. The waves are Doppler-displaced upon the source motion, and superpose into a total, traveling- and in turn a standing- beat wave, or de Broglie phase wave, described by a corresponding total classical wave equation. By back-substitution of the explicitly known total, standing beat wave function and upon appropriate reductions at classic-velocity limit, we separate out from the total a component wave equation describing the kinetic motion of particle, which is equivalent to the Schr\"odinger equation. The Schr\"odinger wave function follows to be the envelope function of the standing beat wave at classic-velocity limit. 
J.X. Zheng-Johansson and P-I. Johansson