I am wondering about the minimum possible uncertainty (standard deviation) in an electron's position (Δx). How precise can one know the electron's whereabouts without creating other sorts of particles and phenomenons.(adsbygoogle = window.adsbygoogle || []).push({});

I know of the localization energy interpretation of the energy uncertainty (ΔE). Using a Heisenberg relation we estimate Δx as

since E=mcΔEΔx≈ħc/2 ⇒ Δx≈ħ/2mc,^{2}for an isolated electron (m is the rest mass). If Δx is smaller than this, extra localization energy manifests itself through other particles.

Now the questions are simple. Is this interpretation valid? What is the actual minimum possible Δx for an isolated electron? Have this been measured?

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# A Minimum uncertainty in electron position

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