Spin 1/2 system - Pure and mixed ensembles

Consider a PURE ensemble of a spin 1/2 system.

Suppose , and the sign of are known.

Show how we may determine the state vector.

Why is it unnecessary to know the magnitude of ?


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Consider a MIXED ensemble of a spin 1/2 system.

Suppose [Sx], [Sy] and [Sz] are known.

Show how we may construct the 2x2 density matrix which characterizes the ensemble.