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Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. [1] [2]: 183–184 Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory.
In physics and chemistry, the spin quantum number is a quantum number (designated s) that describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. It has the same value for all particles of the same type, such as s = 1 / 2 for all electrons.
In quantum mechanics, the total angular momentum quantum number parametrises the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin). If s is the particle's spin angular momentum and ℓ its orbital angular momentum vector, the total angular momentum j is = + .
This would ultimately become the quantized values of the projection of spin, an intrinsic angular momentum quantum of the electron. In 1927 Ronald Fraser demonstrated that the quantization in the Stern-Gerlach experiment was due to the magnetic moment associated with the electron spin rather than its orbital angular momentum. [7]
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.
However the multiplicity equals the number of spin orientations only if S ≤ L. When S > L there are only 2L+1 orientations of total angular momentum possible, ranging from S+L to S-L. [2] [3] The ground state of the nitrogen atom is a 4 S state, for which 2S + 1 = 4 in a quartet state, S = 3/2 due to three unpaired electrons. For an S state ...
There is another type of angular momentum, called spin angular momentum (more often shortened to spin), represented by the spin operator = (,,). Spin is often depicted as a particle literally spinning around an axis, but this is only a metaphor: the closest classical analog is based on wave circulation. [ 2 ]
This is a table of Clebsch–Gordan coefficients used for adding angular momentum values in quantum mechanics.The overall sign of the coefficients for each set of constant , , is arbitrary to some degree and has been fixed according to the Condon–Shortley and Wigner sign convention as discussed by Baird and Biedenharn. [1]
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