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Does uncertainty principle truly represent the “lower bound” of the information we can obtained from a pair of noncommunicable operator?

Background I: Suppose the commonly used non commuting operator $\hat p$ and $\hat x$. The uncertainty principle told us that $\sigma_p\sigma_x\geq \frac{\hbar}{2}$. In standard quantum mechanic ...
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Question on Heisenberg's uncertainty principle [duplicate]

Can we measure limit of precision of measuring wavelength using uncertainty principle? If yes how can we do that?

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