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Homework Help: Heisenberg uncertainty principle

  1. Sep 22, 2007 #1
    Sorry for the other post, I clicked post by mistake

    1. The problem statement, all variables and given/known data
    Find the minimum uncertainty in the length of the year

    2. Relevant equations
    [tex]\Delta[/tex]Px >= [tex]\hbar[/tex]/(2[tex]\Delta[/tex]x


    3. The attempt at a solution
    I did:
    [tex]\Delta[/tex]t = ((([tex]\Delta[/tex]xt)/x)[tex]^{}2[/tex]+((xm)/[tex]\Delta[/tex]Px)[tex]^{}2[/tex])[tex]^{}.5[/tex]

    and then because of the uncertainty principle:
    [tex]\Delta[/tex]t =((([tex]\Delta[/tex]xt)/x)[tex]^{}2[/tex]+((2xm[tex]\Delta[/tex]x)/[tex]\hbar[/tex])[tex]^{}2[/tex])[tex]^{}.5[/tex]

    then I took the derivative dt/d[tex]\Delta[/tex]x to minimize the function. But [tex]\Delta[/tex]x canceled, and I don't get the correct value for h-bar, so I think I did something wrong.

    thanks a lot
     
    Last edited: Sep 22, 2007
  2. jcsd
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