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## Homework Statement

How can we compute the error or uncertainty in measuring an operator O ?

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- Thread starter astrozilla
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How can we compute the error or uncertainty in measuring an operator O ?

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I just thought that there is some mathematical formula or that ΔO (uncertainty) is related somehow to Werner Heisenberg's uncertainty principle.

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The uncertainty of an observable Q is:

[tex](\Delta Q)^2_{\psi}=\langle Q^2 \rangle_{\psi}-\langle Q \rangle^2_{\psi}[/tex]

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astrozilla said:

I just thought that there is some mathematical formula or that ΔO (uncertainty) is related somehow to Werner Heisenberg's uncertainty principle.

It is stupid, because it's first of all poorly worded and then wrongly formulated. As i said above, we measure obervables, but we can't compute the errors, nor the any uncertainty. We can compute some statistical quantities, like mean square deviation, dispersion, mean, probability of an outcome, etc.

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You could, of course, take a bunch of identically prepared systems and perform the same measurement on each, and you would find that the spread in the results reveals this inherent uncertainty in the state.

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