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Non-relativistic limit of Compton scattering -Taylor expansion?

  1. Apr 15, 2013 #1
    1. The problem statement, all variables and given/known data

    In the non-relativistic limit, the equation for Compton scattering is

    v' / v = 1 / (1+x) where x = (hv/mc2)(1-Ω.Ω')

    Show that the change in frequency Δv = v' - v is given by

    Δv / v = -x

    2. Relevant equations

    3. The attempt at a solution

    I rearranged the first equation to get

    v = v'(1 + x)

    v' = v/(1+x)

    This means that

    (v' - v) / v = [(v/(1+x) - (1+x)v'] / [(1 + x)v']

    (v' - v) / v = { [(v/(1+x)] / [(1+x)v'] } - 1

    (v' - v) / v = [1/(1+x)2 (v/v')] -1

    (v' - v) / v = [1/(1+x)] - 1

    Is this an algebra problem, and I can't make it work, or do I need to do a Taylor expansion or something?
  2. jcsd
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