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Total Angular Momentum Quantum NumberThe 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 -
The associated quantum number is the main total angular momentum quantum number j. It can take the following values: -
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) -
the vector's z-projection is given by -
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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