LS coupling and calculating the total angular momentum

[cooper607]

hi all, these days i m going through Arther Beiser's modern physics book where i read about the total angular momentum in many electron atoms..now i could understand the LS coupling and spin orbit effect how they combine to form total angular momentum but if i m given the magnitude of L=2 (orbital angular momentum ) and S=1 (spin angular momentum)

then how can i calculate the configurations they can have and also how can i calculate the J(total angular momentum ) for each configuration ...please help me anyone... i m referring from BESISER'S "PERSPECTIVE OF MODERN PHYSICS "

 

[DrClaude]

The general rule for addition of angular momenta in quantum mechanics is, for $J=L+S$,
$$
J = L+S, L+S-1, \ldots, \left| L - S \right|
$$