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The earliest models for electron spin imagined a rotating charged mass, but this model fails when examined in detail: the required space distribution does not match limits on the electron radius: the required rotation speed exceeds the speed of light. [4]
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 ...
The photon can be assigned a triplet spin with spin quantum number S = 1. This is similar to, say, the nuclear spin of the 14 N isotope, but with the important difference that the state with M S = 0 is zero, only the states with M S = ±1 are non-zero. Define spin operators:
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 fine structure energy corrections can be obtained by using perturbation theory.To perform this calculation one must add three corrective terms to the Hamiltonian: the leading order relativistic correction to the kinetic energy, the correction due to the spin–orbit coupling, and the Darwin term coming from the quantum fluctuating motion or zitterbewegung of the electron.
The superscript three (read as triplet) indicates that the multiplicity 2S+1 = 3, so that the total spin S = 1. This spin is due to two unpaired electrons, as a result of Hund's rule which favors the single filling of degenerate orbitals. The triplet consists of three states with spin components +1, 0 and –1 along the direction of the total ...
The general expression for the spin angular momentum is [1] =, where is the speed of light in free space and is the conjugate canonical momentum of the vector potential.The general expression for the orbital angular momentum of light is =, where = {,,,} denotes four indices of the spacetime and Einstein's summation convention has been applied.
It is the non-relativistic limit of the Dirac equation and can be used where particles are moving at speeds much less than the speed of light, so that relativistic effects can be neglected. It was formulated by Wolfgang Pauli in 1927. [1] In its linearized form it is known as Lévy-Leblond equation.