Consider now a particle which is constrained to move on a circle of
fixed radius R in the x-y plane, so that its position is entirely
determined by the angle 
. From the form of your 
operator
and using the quantum purity test, show that the
wavefunction of the particle in a pure state of angular momentum with
value 
is
Because 
and 
represent the same point, we expect
that 
. Realizing this, what then
are the allowed values of 
in your pure states in 1?
