A Modern Approach to Quantum Mechanics · Problem 3.10

Time Evolution — John S. Townsend

Physics — Quantum Mechanics · spin-half-matrix-mechanics

Problem

Use the matrix representations of the spin-

\frac{1}{2}

angular momentum operators

\hat{S}_x

\hat{S}_y

, and

\hat{S}_z

in the

S_z

basis to verify explicitly through matrix multiplication that

[\hat{S}_x, \hat{S}_y] = i\hbar\hat{S}_z