Standard Model 6: Pauli Matrices

Wolfgang Pauli invented his famous matrices to describe the angular momentum of a spin-1/2 particle back in 1927. You’ll see them in most courses on quantum mechanics. We tend to take them for granted. But where do they come from? Here I derive them from scratch!

There are lots of ways to derive them, and the method I use is not ultimately the best, but it’s the easiest—given that we already have a recipe to describe states of a spin-1/2 particle where it spins in any direction we want.