General Properties of the Electron

Abstract

The fundamental properties of the electron are outlined, and the dualism of its particle and wave nature is discussed. Starting from the particle nature and the concepts of classical mechanics, the principles of Hamilton and Maupertuis are introduced, and the conservation of energy is derived. The concepts of light optics are employed for defining the index of refraction, wavelength, phase and group velocity, and the eikonal. Electron holography, the Aharanov–Bohm effect, and the propagation of the electron wave in macroscopic fields are chosen for demonstrating effects resulting from the wave nature of charged particles.Elementary particles exhibit a wave and a particle nature depending on the specific experiment. Owing to its relatively small rest energy $E_{0}\,=\,m_{\mathrm{e}}{c}^{2} \approx 0.51\,\mathrm{MeV}$, the electron approaches roughly half the speed of light c ≈ 3 ×10⁸ m ∕ s at an accelerating voltage U ≈ 60 kV. Therefore, it is necessary to consider relativistic effects for accelerating voltages larger than about 100 kV. Despite the fact that we can consider the electron as a point-like particle, it has an angular momentum associated with a magnetic moment

$$\mu = \frac{eg\mu _{0}} {2m_{\mathrm{e}}} s = \frac{e\mu _{0}\hslash } {2m_{\mathrm{e}}}.$$

(2.1)

Here, e ≈ 1. 6 10^{− 19} A s and ℏ ≈ 6. 58 ⋅10^{− 16}eV s are the charge of the electron and the Planck constant, respectively; μ₀ is the permeability of the vacuum. We use SI units, which now are universally accepted. From the point of view of classical electrodynamics, a magnetic moment originates from a rotating charge of finite extension forming a magnetic dipole. However, the measured ratio of the magnetic moment and the angular momentum or spin $s = \vert \vec{s}\vert = \hslash /2$ of the electron is twice as large as predicted by classical electrodynamics. This discrepancy, which requires an empirical Lande factorg = 2, can only be explained by means of the relativistic electron theory of Dirac [35, 36]. The spin $\vec{s}$ of the electron is comparable with the polarization of the light.