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    Probabilities in spin measurements

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    The square of the norm of the state

    |psi> = a |up> + b |down>


    |a|^2 + |b|^2

    In the given case with a = sqrt(2/3) and b = i sqrt(1/3) this is clearly equal to 1.

    You can see this also by writing the square of the norm as <psi|psi>. We have:

    <psi| = a* <up| + b* <down|


    <psi|psi> = |a|^2 <up|up> + |b|^2 <down|down> + a*b ...

    Solution Summary

    The expert explains how the formalism of quantum mechanics is used to compute probabilities of outcomes of spin measurements.