Abstract
For the description of an electron by a wave equation, the simplest equation available is the Dirac equation, which in the usual notation reads 
This corresponds to a point particle of charge e, spin ½ħ and magnetic moment eħ/2mc. This equation has met with marked success in describing an electron in static fields and slowly varying fields. For high-frequency fields, however, there are indications that the description is only an approximate one, and that allowance should be made for the finite extension of the electron.
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References
Eliezer, C. J., Proc. Roy. Soc., A, 194, 543 (1948); Proc. Camb. Phil. Soc., 46, 199 (1950).
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ELIEZER, C. Wave Equation of the Electron. Nature 167, 78–79 (1951). https://doi.org/10.1038/167078b0
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DOI: https://doi.org/10.1038/167078b0
