Is the Formula for Spin Also True for Angular Momentum?

[Cosmossos]

Hello
Here is the known formula for the spin: S=0.5*[STRIKE]h[/STRIKE]*$$\sigma$$
is this formula correct also to the orbital Angular momentum (L) and to the total Angular momentum?
I think it is correct because S,L,J operators that belong to Lie algebra/group.
Is it true?

 

[strangerep]

Here is the known formula for the spin: S=0.5*[STRIKE]h[/STRIKE]*$$\sigma$$
is this formula correct also to the orbital Angular momentum (L) and to the total Angular momentum?
I think it is correct because S,L,J operators that belong to Lie algebra/group.
Is it true?

No. The orbital angular momentum has a special form:

$${\bm L} ~=~ {\bm Q} ~\times~ {\bm P}$$

where Q and P satisfy the usual Heisenberg commutation relations.
This extra restriction causes a corresponding restriction in the
possible eigenvalues of orbital angular momentum, namely that
only integer values are allowed.

Details can be found in Ballentine, pp169-170.