A spin- particle is prepared in and rotated by about the axis.

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Symmetry, angular momentum and spin · Symmetry, angular momentum and spin

The Structure of Quantum Mechanics, Ch Angular momentum from the rotation group

Problem

A spin-

\tfrac12

particle is prepared in

|\tfrac12,\tfrac12\rangle

and rotated by

\beta=\pi/3

about the

y

axis. ((a)) Using the Wigner matrix

d^{(1/2)}(\beta)

, find the probabilities that a measurement of

\hat S_z

then gives

+\hbar/2

and

-\hbar/2

. ((b)) Write the rotated state if the angle is instead

\beta=2\pi

, and give the same two probabilities for it.