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Momentum/Real space

  1. Sep 27, 2009 #1
    1. The problem statement, all variables and given/known data
    Suppose at t = 0, a system is in a state given by the wavefunction,
    [tex]\Psi[/tex](x,0)=1/[tex]\sqrt{a}[/tex] for |x|<a/2
    and [tex]\Psi[/tex](x,0)=0 otherwise
    If, at the same instant, the momentum of the particle is measured, what are the
    possible values that can be found and with what probability?




    2. Relevant equations
    Fourier transformations b/w momentum and real spaces
    [tex]\Psi[/tex](x,0)=[tex]\int[/tex]A(k)eikxdk
    A(k)=[tex]\frac{1}{2\Pi}[/tex][tex]\int[/tex][tex]\Psi[/tex](x,0)e-ikxdx




    3. The attempt at a solution
    I have little idea of how to solve this problem. I know that the wave packet is a superposition of waves but i have no idea how to get momentum values. Here is my pathetic fail attempt:
    [tex]\Delta[/tex]x[tex]\Delta[/tex]p>h/4[tex]\Pi[/tex]
    but [tex]\Delta[/tex]x<a/4
    => [tex]\Delta[/tex]p>h/(4[tex]\Pi[/tex][tex]\Delta[/tex]a)
    I know its seriously wrong.
     
  2. jcsd
  3. Sep 27, 2009 #2
    The A(k) can be viewed as probability amplitudes in momentum space. That is A*(k)A(k) is the probability for a value k. So calculate these things and when you do ask yourself what the form of the expressions can tell you about the range k can have (and what happens at special values of k).
     
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