Lets say we put an electron in a box (spherical) which has a radius ##r##. I want to know if position uncertainty ##\Delta x = r## or is it ##\Delta x = 2r##?(adsbygoogle = window.adsbygoogle || []).push({});

I need to know this to corectly calculate 1st the momentum uncertainty ##\Delta p=\frac{\hbar}{2\Delta x}## and 2nd that kinetic energy uncertainty ##\Delta E_k## using the Lorentz invariant like this:

\begin{align}

\Delta E^2 &= \Delta p^2 c^2 + {E_0}^2\\

\Delta E &= \sqrt{\Delta p^2 c^2 + {E_0}^2}\\

\Delta E_k + E_0 &= \sqrt{\Delta p^2 c^2 + {E_0}^2}\\

\Delta E_k &= \sqrt{\Delta p^2 c^2 + {E_0}^2} - E_0\\

\end{align}

Furthermore. Can anyone elce confirm that this is the proper way to get the kinetic energy uncertainty ##\Delta E_k##. Is it ok that uncertainty for full energy ##\Delta E## all comes from the uncertainty in kinetic energy ##\Delta E_k## and none from rest energy (infront of which i wrote no deltas) ##E_0##?

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# Uncertainty of an electron in a core

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