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Total angular momentum quantum number
In quantum mechanics, the total angular quantum momentum numbers parameterize the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin).
Additional recommended knowledge
If s is the particle's 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 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.
The total angular momentum corresponds to the Casimir invariant of the Lie algebra SO(3) of the three-dimensional rotation group.
|This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Total_angular_momentum_quantum_number". A list of authors is available in Wikipedia.|