Inference of Schr\"odinger's Equation from Classical-Mechanical Solution

TL;DR

This paper derives the Schrödinger equation from a classical wave framework involving oscillatory charges and electromagnetic waves, showing the quantum wave function as an envelope of classical wave phenomena.

Contribution

It presents a novel derivation of the Schrödinger equation from classical wave solutions of oscillatory charges and electromagnetic waves in a potential field.

Findings

Schrödinger equation emerges as a component wave equation in a classical wave model.

The quantum wave function is shown to be an envelope of a classical standing beat wave.

Classical wave solutions can reproduce quantum mechanical behavior at low velocities.

Abstract

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.