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The Spinning Electron

John Lekner
School of Chemical and Physical Sciences, Victoria University of Wellington, Wellington, New Zealand

Published 2022-07-18


  • Electron,
  • Spin,
  • Spinor

How to Cite

Lekner, J. (2022). The Spinning Electron. Substantia. https://doi.org/10.36253/Substantia-1630


The notion introduced by Ohanian that spin is a wave property is implemented, both in Dirac and in Schrödinger quantum mechanics. We find that half-integer spin is the consequence of azimuthal dependence in two of the four spinor components, relativistically and non-relativistically. In both cases the spinor components are free particle wavepackets; the total wavefunction is an eigenstate of the total angular momentum in the direction of net particle motion. In the non-relativistic case we make use of the Lévy-Leblond result that four coupled non-relativistic wave equations, equivalent to the Pauli-Schrödinger equation, represent particles of half-integer spin, with g-factor 2. An example of an exact Gaussian solution of the non-relativistic equations is illustrated.


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