We show that the classical wave equation for a single oscillatory charge which may be in general also traveling in a potential field $V$ , embraces a separable component equation describing the particle dynamics. We show the latter is equivalent to Schr\\"odinger's wave equation. In this first paper of a series we infer Schr\\"odinger's wave equation for such a charged system in zero potential field.We show that the classical wave equation for a single oscillatory charge which may be in general also traveling in a potential field $V$, embraces a separable component equation describing the particle dynamics. We show the latter is equivalent to Schr\\"odinger's wave equation. In this first paper of a series we infer Schr\\"odinger's wave equation for such a charged system in zero potential field.

Nov 15, 20040 citations

Schrödinger's Equation and Quantum Mechanics

акустика Механика

Betascript Publishing eBooksAug 2, 20100 citations

Inference of Schrödinger's Equation from Classical-Mechanical Solution

J. X. Zheng-Johansson, Johansson, P-I.

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 Schrödinger equation. The Schrödinger wave function follows to be the envelope function of the standing beat wave at classic-velocity limit.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 Schrödinger equation. The Schrödinger wave function follows to be the envelope function of the standing beat wave at classic-velocity limit.

arXiv:physics/0411134Nov 15, 20042 citations

We show that the classical wave equation for a single oscillatory charge which may be in general also traveling in a potential field

V

, embraces a separable component equation describing the particle dynamics. We show the latter is equivalent to Schr\\"odinger's wave equation. In this first paper of a series we infer Schr\\"odinger's wave equation for such a charged system in zero potential field.

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 Schrödinger equation. The Schrödinger wave function follows to be the envelope function of the standing beat wave at classic-velocity limit.