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).
It can take the following range of values, jumping only in integer steps:[1]
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)
where mj is the secondary total angular momentum quantum number, and the
The total angular momentum corresponds to the Casimir invariant of the Lie algebra so(3) of the three-dimensional rotation group.
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