The Spinning Electron in Wave Mechanics

Abstract

THE new wave mechanics admits the existence in physical phenomena of a variable quantity that satisfies a special differential equation. According to Schrödinger, this function is such that the product , where is the conjugate complex quantity, is the electrical density. On the contrary Bateman (NATURE, 118, 839) has recently shown that, by considering two functions, each of which satisfies the wave equation, it is possible to determine the potentials a and of the electromagnetic field. Starting from Bateman's considerations, de Broglie (C.R. 184, 81) has shown that the values calculated with this theory coincide with those of Maxwell's theory if one admits that the frequency of the fundamental functions be very high and that the considered phenomenon be nearly stationary in relation to this frequency. De Broglie, however, has shown that, given the waveequation putting in the place of the function the two ₁ = A÷r cos 2₀t, ₂= Bsin 2₀t, and introducing the potentials the results verify Lorentz's equation We thus obtain for the fields E and H the expressions that is, the characteristic values of a pole of charge k.