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Conceptual question about wavefunctions/momentum

  1. Mar 17, 2008 #1
    Hi all,

    If I have the wave function of a system, then the expectation of position is easily visualized as the centroid of the distribution.

    Does anyone know how to visualize the expectation of velocity given just the postion-space wavefunction (real and imaginary parts)
  2. jcsd
  3. Mar 17, 2008 #2


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    Er... couldn't you just use the expectation value of the momentum, i.e. <p>? I'm assuming that you know what p operator is in the real-space representation.

  4. Mar 18, 2008 #3


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    I do know what it is!
    p = -i \frac{d}{dx}

    ...always. since p generates translations in space.
  5. Mar 18, 2008 #4
    What i'm going to tell you is in a contradiction with your question, cause you say, you only have realspace wavefunction. However, i find it very instrumental to imagine it in this way:

    Take the realspace wavefunction. Do its fourier transform. You obtain a k-space wavefunction. In this representation, the momentum (~velocity) operator has exactly the same form as position operator in realspace representation. So the centre of this function is the mean momentum value.
  6. Mar 19, 2008 #5
    yes,I agree this.
    Use foiurier transformation to get the wavefunction in the momentum representation.
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