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Uncertainty in the position of a particle, and momentum question

  1. Feb 26, 2009 #1
    Hi all,

    I just can't wrap my head around this one. It should be fairly easy, but i'm lost!

    1. The problem statement, all variables and given/known data
    Suppose that the uncertainty in the position of a particle is of the order of its de Broglie wavelength. Show that in this case the uncertainty in its momentum is of the order of it's momentum.

    2. Relevant equations

    Not 100% sure...

    Delta x is similar to the wavelength
    Delta p is similar to Plancks constant over wavelength
    Therefore delta x delta p are similar to Plancks constant

    3. The attempt at a solution
    Well I can see how delta x and delta p can be related together to the wavelength, but after that I'm lost.

    Any help much appreciated! I'm a B.Sc Mechanical Engineer doing an entry level nuclear physics course and I'm holding on... just.
  2. jcsd
  3. Feb 26, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Yes, so you almost got it.

    [tex]\Delta x \sim \lambda[/tex]
    If the uncertainty relation is near the minimum value, then
    [tex]\Delta x \Delta p \sim \hbar[/tex]

    So what is [itex]\Delta p[/itex] then. What is [itex]\lambda[/itex] in terms of p?
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