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Normalizing a wave packet - cannot understand the solution

  1. Sep 20, 2010 #1
    This question is about normalizing a wave packet, this is actually the solution and I couldn't understand 2 points.

    - I cannot see how the red encircled part do not diverge to infinity.

    - And I cannot understand how the very last line is derived from the 2nd last one.

    For the second one I tried to call i(po-px) as A and 1/(deltaX) B but that did not lead anywhere.

  2. jcsd
  3. Sep 20, 2010 #2
    For the red box
    e^{i \alpha x - \beta x} = e^{i \alpha x}e^{-\beta x}
    for x -> infinity: the first term oscillates between 1 and -1 (in accordance with euler's equation), but the second term approaches zero. So the whole thing approaches zero, and you're just left with the evaluation at x = 0.

    And for the penultimate to ultimate lines, you just have to get a common denominator to combine the fractions; a bunch of stuff will cancel.... you multiply through by delta X / delta X
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