Uncertainties & Total Angular Momentum

[Sekonda]

Hey,

My question is on determining an 'uncertainty' quantity using total angular momentum operators in the x,y and z directions where we know the commutation relations between the x,y and z directions of the total angular momentum operators.

I'm not really sure where to go with this at all, I let the commutator given act on a state |m> i.e. an eigenfunction of J(z)

$$[\hat{J_{x}},\hat{J_{y}}]|m>=i\hbar\hat{J_{z}}|n>=i\hbar m|m>$$

So the commutator must equal i*hbar*m, right? Anyway I'm not sure if this is even a correct way to begin, but it should be pretty straightforward however I haven't really come across a question like this before.

By the way I replaced subscripts 1,2,3 with x,y and z repsectively.

Thanks for any help!
SK

 

[Sekonda]

Woops, the equation should read:

$$[\hat{J_{x}},\hat{J_{y}}]|m>=i\hbar\hat{J_{z}}|m>=i\hbar m|m>$$

not 'n' ket but 'm' ket.

Sorry...

SK