3) Derivation of the hypothesis about the amplitudes.----[Return home ]

In the derivation of the electron wave structure in motion, and especially the de Broglie wave , an hypothesis has been used that the amplitudes of the divergent wave has the same amplitude as the convergent wave for any particular position (x,y,z,t).

If we consider fully valid that the wave structure is the same in the moving Einsteinian frame with the electron as when the electron is at rest in the rest frame, the amplitude of any travelling wave for a particular value Ro' of r in the moving frame has a spherical symetry which may be represented by the following equation: A'(r')=A'(Ro').

This equation written in the rest frame where the electron is in motion:

, shows that the amplitude is constant for each wave on the surface of an ellipsoid of main axis Ro' and of shortest axis:

sqrt[sq(x-vt)]=Ro'.sqrt(1-bb)

Thus, the amplitudes of the standing waves are the same for any value of r , but in the rest frame with an ellipsoidal symetry.

This result is very important to understand later the derivation of the Maxwell's equations.

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