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Homework Help: Find momentum of wavefunction

  1. Oct 19, 2011 #1
    1. The problem statement, all variables and given/known data

    Wavefunction is of form:
    ψ(x) = eikx
    Find momentum and energy of this state.

    2. Relevant equations
    Fourier transform of ψ(x) to get to momentum space
    or is it
    <p> = integral from -infinity to infinity of ψ* (h/i) * derivative wrt x of ψ dx

    3. The attempt at a solution

    I initially tried the second approach, but it didn't work, I got an infinite answer. Someone said to instead convert the function to momentum space, I used the Fourier transform but when I do that, my integral in the Fourier transform is -infinity to infinity of an oscillating function that doesn't decrease and is undefined.

    I have no idea now how to proceed. I've worked on this question for hours, I searched the textbook, google, etc. and could not find anything useful.
  2. jcsd
  3. Oct 19, 2011 #2


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    Staff Emeritus
    Science Advisor
    Homework Helper
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    Hint: One representation of the Dirac delta function is
    [tex]\delta(x-x_0) = \frac{1}{2\pi}\int_{-\infty}^\infty e^{-ik(x-x_0)}\,dk[/tex]

    Another way you could approach the problem is to simply apply the momentum operator to that function and interpret what the equation means.
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