8) For a spin-1 particle, measurement of S, results in any of the three possible values (-1, 0 1). In a certain situation, it is found that the probabilities to obtain 1 are equal.
a) Write the most general quantum state that describes this situation.
b) Calculate the uncertainty S, for that state.
c) Suppose it also happens that Sy = 0. Write the most general quantum state that describes this situation.
d) Show that under the above conditions ([A, Sy) = 0 for arbitrary operators A.