# QM: Spin and Angular Momentum.

1. Oct 26, 2011

### doublemint

Hello All,

Right now, I am trying to complete my QM assignment, but I am getting confused about the notation.

So, the generalized angular momentum operator is represented as $\hat{J}$ and -j is the quantum # associated with the magnitude and $m_{j}$ is the quantum # associated with the projection of the angular momentum projection.
Then given j=2, $m_{j}$=-2,-1,0,1,2
So now onto spin. The spin operator is $\hat{S}$ and similar s is the magnitude of the spin and $m_{s}$ is the projections. Then given s=1/2, $m_{s}$=1/2,-1/2
So far so good right?
Now what is confusing to me is this: the question is asking for the expectation of the three components of angular momentum of a spin 5 particle. Does it mean s=5 or j=5?

Another question is what does it mean by "the quantum number associated with the magnitude of the spin for a particle"? Are they asking for s?

Thanks
DoubleMint

2. Oct 27, 2011

### dextercioby

I think they discard the orbital angular momentum, so that j=s=5. The magnitude is usually seen as the eigenvalue of S2.