# 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.

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#### Solution Preview

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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 ?

Answer.-

The corresponding Eigen states for a ½ spin system are just

In other words the state ...

#### 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.