A Modern Approach to Quantum Mechanics · Problem 3.9

Time Evolution — John S. Townsend

Physics — Quantum Mechanics · uncertainty-relations-angular-momentum

Problem

Calculate

\Delta S_x

and

\Delta S_y

for an eigenstate of

\hat{S}_z

for a spin-

\frac{1}{2}

particle. Check to see if the uncertainty relation

\Delta S_x \Delta S_y \geq \hbar|\langle S_z\rangle|/2

is satisfied. Repeat your calculation for an eigenstate of

\hat{S}_x