Z component of spin angular momentum quantum number values

[LostConjugate]

Hello,

What prevents the S_z quantum number from having a value of zero? With a standard angular momentum system the quantum number can have values between -l and +l.

 

[dextercioby]

Technically, in nonrelativistic QM a spin 1 particle can have m_s = 0. However, a particle with spin 1 is properly described in a relativistic context, where m_s loses its nonrelativistic meaning and the concept of helicity steps in.

 

[LostConjugate]

What about spin of 1/2? It should still be able to have -1/2, 0, and 1/2. Zero in the z component as a quantum number just means that the angular momentum cone is roughly pointing somewhere in the xy plane.

 

[dextercioby]

No, no, the weights must differ by 1, so it's -1/2, then +1/2.

 

[LostConjugate]

No, no, the weights must differ by 1, so it's -1/2, then +1/2.

Oh, so it is a consequence of the 1/2 angular momentum itself. How is a general direction of the angular momentum in the xy plane represented then?