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Position of a proton in Quantum mechanics.

1. Homework Statement
Find the maximum accuracy that can be found to a proton's position without changing it's (not-realativistic) kinetic energy by more that 1 keV

I think this involves heisenberg's uncertainty principle [tex]\Delta x\Delta p=hbar/2[/tex] but im not sure at all.

Now to find the momentum p of a non-realativistic kinetic energy we can use [tex]E(kinetic) = 1/2mv^2 = p^2/2m[/tex]
which gives [tex]p = \sqrt{}2mE[/tex]
however this is as far as i got.
Last edited:
Usually, professors expect you to realize that [tex]p\ge\Delta p[/tex]. Use this and see whether the answer matches!
That is, use that
[tex]p\Delta p=m\Delta E[/tex]
[tex]\Rightarrow \Delta p\le\sqrt{m\Delta E}[/tex]
[tex]\Rightarrow \Delta x\ge \frac{\hbar}{2\sqrt{m\Delta E}}[/tex]

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