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The value of 2 arises from the Dirac equation, a fundamental equation connecting the electron's spin with its electromagnetic properties; and the deviation from −2 arises from the electron's interaction with the surrounding quantum fields, including its own electromagnetic field and virtual particles.
The general form of wavefunction for a system of particles, each with position r i and z-component of spin s z i. Sums are over the discrete variable s z , integrals over continuous positions r . For clarity and brevity, the coordinates are collected into tuples, the indices label the particles (which cannot be done physically, but is ...
The electron mobility is defined by the equation: =. where: E is the magnitude of the electric field applied to a material, v d is the magnitude of the electron drift velocity (in other words, the electron drift speed) caused by the electric field, and; μ e is the electron mobility.
The spin magnetic moment of the electron is =, where is the spin (or intrinsic angular-momentum) vector, is the Bohr magneton, and = is the electron-spin g-factor. Here μ {\displaystyle {\boldsymbol {\mu }}} is a negative constant multiplied by the spin , so the spin magnetic moment is antiparallel to the spin.
The atom would then be pulled toward or away from the stronger magnetic field a specific amount, depending on the value of the valence electron's spin. When the spin of the electron is + + 1 / 2 the atom moves away from the stronger field, and when the spin is − + 1 / 2 the atom moves toward it. Thus the beam of silver atoms is ...
These equations say respectively: a photon has zero rest mass; the photon energy is hν = hc|k| (k is the wave vector, c is speed of light); its electromagnetic momentum is ħk [ħ = h/(2π)]; the polarization μ = ±1 is the eigenvalue of the z-component of the photon spin.
The formula for evaluating the drift velocity of charge carriers in a material of constant cross-sectional area is given by: [1] u = j n q , {\displaystyle u={j \over nq},} where u is the drift velocity of electrons, j is the current density flowing through the material, n is the charge-carrier number density , and q is the charge on the charge ...
For example, the Dirac Hamiltonian for a particle of mass m and electric charge q in an electromagnetic field (described by the electromagnetic potentials φ and A) is: ^ = [(^) + +], in which the γ = (γ 1, γ 2, γ 3) and γ 0 are the Dirac gamma matrices related to the spin of the particle. The Dirac equation is true for all spin-1 ⁄ 2 ...