How to Create Angular Momentum Eigenstates
Find the Eigenfunctions of Lz in Spherical Coordinates
How Spin Operators Resemble Angular Momentum Operators

Pauli Matrices

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 Sx, Sy, and Sz written in terms of Pauli matrices,


Given that the eigenvalues of the S2 operator are


and the eigenvalues of the Sz 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 <i>z</i> projection.
Spin magnitude and z projection.

Here’s what the Pauli matrices look like for the operators Sx, Sy, and Sz:


Now you can write Sx, Sy, and Sz in terms of the Pauli matrices like this:

  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
Spin One-Half Matrices
How to Find Angular Momentum Eigenvalues
How to Change Rectangular Coordinates to Spherical Coordinates
Find the Eigenvalues of the Raising and Lowering Angular Momentum Operators
Find the Missing Spot with the Stern-Gerlach Experiment