If we rotate our coordinate system by 90 degrees about the z axis,
the old x axis becomes the new -y axis.
So we would expect that the state with angular momentum
in the x direction,
will rotate into
within a phase factor.
Lets do the rotation.
The rotated state is.
Now, what remains is to check whether this state is the one we expect.
We find that state by solving the eigenvalue problem.
, we get the unnormalized result.
Jim Branson 2013-04-22