Quantum Physics


Derivation of the Fine Structure Constant from the Electron Wave Function

Authors: Declan Traill

The fine structure constant α characterizes the strength of the electromagnetic interaction between elementary charged particles. Its value can be derived from the wave function for the electron. The electron wave function describes a field of Harmonic Oscillators which have the energy of the rest-mass of an electron. However, it takes time for such an Oscillator to complete a cycle of oscillation, so during this time the electromagnetic field that propagates into space from the Oscillator has expanded away from its source to cover the surface area of a three-dimensional shape. Therefore, the amplitude of the oscillations has been reduced before it can interact with its surrounding environment. The amount of this diminution is what the fine structure constant α represents. The actual value of α also depends on the fact that the source of the spreading energy is rotating Harmonic Oscillators. Classically, a point source will spread evenly in all directions and the intensity will diminish with Inverse-Square Law. But in the actual electron wave-function, the Harmonic Oscillators are rotating whilst expanding, causing the area that the energy spreads out over to be that of an expanding cone as well as that of a sphere. The area of this shape is greater than that of a simple sphere; this is what causes the fine structure constant α to have the value that it does.

Comments: 7 Pages.

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Submission history

[v1] 2019-07-10 00:17:23
[v2] 2019-07-10 20:02:29
[v3] 2019-07-11 19:12:03
[v4] 2019-07-12 17:20:50
[v5] 2019-07-14 22:28:35

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