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Hi all-given
This is unnecessarily complicated and confusing. The answer is
that a 1-particle bosonic (integer spin) state is invariant under a
360 degree rotation. A 1-particle fermionic state changes sign under such
a rotation.
End of story. For more detail see Weinberg, Vol. I, p. 89, where
you will see that the result is not quantum-mechanical but has to do
with representations of the Poincare' group.
Regards,
Jack
On Fri, 22 Dec 2000, Robert B Zannelli wrote:
OK Let me see if I get this. The number of a particles' eigenstates is
and ourby the equation n=2s+1. Any particle will be not be in any defined state
until a measurement is made of that particles spin. An unmeasured particle
will be in a superposition of all it's possible eigenstates. For a spin 2
particle there are 5 possible states which are-2,-1,0,1,2 . Now if we take
the vector in the Hilbert space which defines the mix of these states
need a2 spin particle superposition states consist of only amplitudes in even
number states then a 180 degree rotation will be a complete cycle. Should
there be any probability amplitude for any odd numbered state we would
360 degree rotation to complete a full cycle. In any case a 360 degree
rotation always returns the same amplitude.