Total Angular Momentum Quantum Number

The total angular quantum momentum numbers parameterize the total angular momentum of a given electron, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin). If s is the electron spin angular momentum and l its orbital angular momentum vector, the total angular momentum j is
\mathbf j = \mathbf s + \mathbf l
The associated quantum number is the main total angular momentum quantum number j. It can take the following values:
|l - s| \le j \le l + s
where l is the azimuthal quantum number (parameterizing the orbital angular momentum) and s is the spin quantum number (parameterizing the spin). The relation between the total angular momentum vector j and the total angular momentum quantum number j is given by the usual relation (see angular momentum quantum number)
\Vert \mathbf j \Vert = \sqrt{j \, (j+1)} \, \hbar
the vector's z-projection is given by
j_z = m_j \, \hbar
where mj is the secondary total angular momentum quantum number. It ranges from −j to +j in steps of one. This generates 2j + 1 different values of ''mj.

See also

External links

* LS and jj coupling

 

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