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

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 m_j 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 m_j.

See also

• Principal_quantum_number
• orbital angular momentum quantum number
• magnetic quantum number
• spin quantum number
• Angular momentum coupling

External links

• Vector model of angular momentum
• LS and jj coupling