Spin Matrix for Arbitrary Spin: A Closer Look

[captain]

i am having trouble understanding if the spin matrix S_i (the i th compenent of the spin matrix which is h-bar divided by 2pi times i th pauli spin matrix) is only for spin 1/2 and if it is then what would be the spin matrix for an arbitrary spin?

 

[malawi_glenn]

If you know how the pauli matrices are derived, I am sure you can figure out how to construct spin matrices for higher spin.

 

[meopemuk]

i am having trouble understanding if the spin matrix S_i (the i th compenent of the spin matrix which is h-bar divided by 2pi times i th pauli spin matrix) is only for spin 1/2 and if it is then what would be the spin matrix for an arbitrary spin?

A hint: particles of different spin are closely associated with unitary irreducible representations of the rotation group. There are representations of integer dimensions: 1,2,3,4,... which correspond to spin values 0, 1/2, 1, 3/2,... So, in order to build spin matrices for spin 1 you can build a 3-dimensional irreducible unitary representation of the rotation group. Then 3 Hermitean generators S_i of this representation will be the spin matrices you are interested in.

Eugene.