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Spin 1/2 System: Pure and Mixed Ensembles

Consider a pure ensemble of a spin 1/2 system.
Suppose <Sx>, <Sz> and the sign of <Sy> are known.
Show how we may determine the state vector.
Why is it unnecessary to know the magnitude of <Sy> ?

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.

Solution Summary

This solution provides clarification on pure and mixed ensembles of a spin 1/2 system. It discusses concepts like the state vector, magnitude, and density.

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