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References
We put the velocity of light c equal to 1.
The calculation presented below was performed for the first time by N.B. Narozhny (1979).
In this and two next subsections we follow the work by I. B. Khriplovich, A. I. Milshtein, A. S. Yelkhovsky (1994).
Let us recall that once this coincidence proved to be extremely important for the correct interpretation of the Rutherford experiments and for the creation of quantum mechanics.
Let us note that for a charged scalar particle the corresponding ground state energy is\(E = mc^2 \sqrt{1/2 + \sqrt{1/4-(Ze^2/\hbar c)^2}}.\)
The discussion of this problem looks proper since from time to time, at least in folklore, one comes across absolutely absurd attempts to explain this ratio.
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(2008). Quantum Electrodynamics. Again Minimum Calculations. In: Theoretical Kaleidoscope. Lecture Notes in Physics, vol 747. Springer, New York, NY. https://doi.org/10.1007/978-0-387-75252-5_6
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