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    Spin 1/2 System: Pure and Mixed Ensembles

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    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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    https://brainmass.com/physics/physics-measurements/spin-system-pure-mixed-ensembles-180617

    Solution Preview

    Please refer to the attached documents.

    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.

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