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I Wave packet integral question

  1. Nov 7, 2016 #1
    upload_2016-11-7_15-20-40.png

    Hi,

    what kind if integration used on equation 1 so it turned into equation 2? this does not look like integration by parts. and where (x-x0) appeared from instead of (k-k0) ?

    thanks for your help.
     
  2. jcsd
  3. Nov 7, 2016 #2

    DrClaude

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    Staff: Mentor

    No integration was done. For instance, for the imaginary term, you multiply by the right-hand side by ##\exp[i k_0(x-x_0)] \exp[-i k_0(x-x_0)]##, and move the second exponential inside the integral sign.
     
  4. Nov 7, 2016 #3

    andrewkirk

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    No integration has been done yet. It's the old mathematical trick of multiplying and dividing by the same thing.
    Outside the integral is a factor of
    $$\exp\left[-\frac{(x-x_0)^2}2(\Delta k)^2\right]$$
    and inside the integral is a factor of the reciprocal
    $$\exp\left[\frac{(x-x_0)^2}2(\Delta k)^2\right]$$
    These cancel each other out.

    They can be freely moved through the integral sign because they do not involve the integration variable ##k##.

    EDIT: Darn, Dr Claude jinxed me. Now I'm not allowed to talk for the rest of the day.
     
  5. Nov 7, 2016 #4

    dextercioby

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    I bet you are reading from a Russian book translated into English decades ago.
     
  6. Nov 8, 2016 #5
    :D I have many of those books too.
    But this image is from David Bohm's Quantum Theory.
     
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