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Uncertainty principle - just want to check my method

  1. May 19, 2010 #1
    1. The problem statement, all variables and given/known data

    Estimate the kinetic energy of a constituent quark of mass 300 MeV/c^2 confined insdide a proton of radius 1 fm

    2. Relevant equations

    Heisenberg's uncertainty principle [tex]\Delta x \Delta p \approx \hbar[/tex] (1)
    Kinetic energy [tex] T=\frac{p^2}{2m}[/tex] (2)

    3. The attempt at a solution

    So we've got [tex]\Delta x[/tex]. So we can rearrange (1) to get [tex]\Delta p[/tex]

    Then we need to use (2). Is it OK to just say [tex]\Delta T = \frac{\Delta p^{2}}{2m}[/tex]

    Alternatively could we use the relation that delta T = dT/dp delta p but then we'd need to know p as well. And how would we then use this to get T?

    This should be easy, but I never know when to use the second method using differentiation and when not to. Cheers.
  2. jcsd
  3. May 20, 2010 #2
    That is perfectly fine.
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