In quantum physics, when you work with spin eigenstates and operators for particles of spin 1/2 in terms of matrices, you may see the operators S* _{x}*, S

*, and S*

_{y}*written in terms of*

_{z}*Pauli*matrices,

Given that the eigenvalues of the S^{2} operator are

and the eigenvalues of the S_{z} operator are

you can represent these two equations graphically as shown in the following figure, where the two spin states have different projections along the *z* axis.

Spin magnitude and

*z*projection.Here’s what the Pauli matrices look like for the operators S* _{x}*, S

*, and S*

_{y}*:*

_{z}Now you can write S_{x}, S_{y}, and S_{z} in terms of the Pauli matrices like this: