The chapter multiplies out and in full to get

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · The formalism of quantum mechanics · Symmetry, angular momentum and spin

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Spin one-half, the Pauli matrices and two-level systems

Problem

The chapter multiplies out

\sigma_x\sigma_y

and

\sigma_y\sigma_x

in full to get

[S_x,S_y] = i\hbar S_z

, and states that

[S_y,S_z] = i\hbar S_x

and

[S_z,S_x] = i\hbar S_y

follow the same pattern without carrying out the multiplication. Multiply out

\sigma_z\sigma_x

and

\sigma_x\sigma_z

in full, and use the result to verify

[S_z,S_x] = i\hbar S_y