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Uncertainty Principle and dart of mass

  1. Aug 6, 2015 #1
    1. The problem statement, all variables and given/known data
    A dart of mass ##m## is dropped from a height ##l##. Formulate the uncertainty principle and estimate the minimum limitations, set by the uncertainty principle, of the accuracy that can be achieved in the lateral ##x## position after falling, given an original uncertainty ##\Delta x##, and no original uncertainty in y.

    2. Relevant equations


    3. The attempt at a solution
    The time to drop is ##\sqrt{2l/g}##. With uncertainty the dart hits the ground at a distance ##R## where:

    ##R=\Delta x+\sqrt{2l/g}\space \Delta p/m \geq\Delta x +\sqrt{2l/g}\space \hbar/2m\Delta x##

    This next part I found from a book but I don't understand how its got from above:

    ##\Delta x=(l\hbar^2/2m^2g)^{\frac{1}{4}}##

    with ##R\geq(8l\hbar^2/m^2g)^{\frac{1}{4}}##

    Could anyone clarify how ##\Delta x## and ##R## were found?
     
    Last edited: Aug 6, 2015
  2. jcsd
  3. Aug 6, 2015 #2
    Please review the statement of the problem, it seems that the last sentence is not finished and maybe we miss important data.
     
  4. Aug 6, 2015 #3
    Hey soarce I edited the omission.
     
  5. Aug 6, 2015 #4
    Your derivation seems correct. Can you give us the reference from where you took the formula for ##\Delta x##?
     
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