A spin one-half is precessed actively about the -axis through

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Quantum Mechanics · Symmetry, angular momentum and spin

Invariance, Ch Lie groups and Lie algebras: rotations, SU(2) and the double cover

Problem

A spin one-half is precessed actively about the

z

-axis through

\theta = 270^\circ

. Using

U(\theta) = \exp(-\mathrm i\theta\sigma_z/2) = \cos(\theta/2)\mathsf 1 - \mathrm i\sin(\theta/2)\sigma_z

, write down

U(270^\circ)

explicitly, and state the value of

\theta

for which

U(\theta)

first returns to

+\mathsf 1