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Position of a proton in Quantum mechanics.

  1. Mar 25, 2009 #1
    1. The problem statement, all variables and given/known data
    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: Mar 25, 2009
  2. jcsd
  3. Jun 30, 2009 #2
    Usually, professors expect you to realize that [tex]p\ge\Delta p[/tex]. Use this and see whether the answer matches!
     
  4. Jun 30, 2009 #3
    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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