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Derive the Compton I'm stuck :[

  1. Jan 18, 2009 #1
    1. The problem statement, all variables and given/known data

    Derive the compton equation.

    2. Relevant equations
    [tex]\lambda[/tex]` - [tex]\lambda[/tex] = h/ mc (1 - cos[tex]\theta[/tex])
    E = hf = hc/[tex]\lambda[/tex]

    3. The attempt at a solution
    Okay, I'm sorry this is so long, I'll try and make it as concise as it is possible for a whole blather of random crap to be :]

    Conservation of momentum components:
    h/[tex]\lambda[/tex] = h/[tex]\lambda[/tex]`(cos[tex]\theta[/tex]) + Pe(cos[tex]\psi[/tex])
    0 = h/[tex]\lambda[/tex]`(sin[tex]\theta[/tex]) - Pe(sin[tex]\psi[/tex])

    After some combining, squaring, and the like (getting rid of [tex]\psi[/tex]):
    Pe2 = (h/[tex]\lambda[/tex])2 - (h/[tex]\lambda[/tex]`)2cos2[tex]\theta[/tex] + (h/[tex]\lambda[/tex]`)2sin2[tex]\theta[/tex] - (h/[tex]\lambda[/tex])(h/[tex]\lambda[/tex]`)cos[tex]\theta[/tex]

    E2 = p2c2 + ER2
    P2 = (E2 - ER2)/c2

    So I plug that into my momentum (I'm not gonna write the righthand side of the equation while i show what I did w/ that)

    (E2 - ER2)/c2 = ...
    ((hc/[tex]\lambda[/tex])2 - (mc2)2)/c2 = .
    I tried to get rid of the denominator 'c'...
    (h/[tex]\lambda[/tex])2 - m2c2 = ...

    (m2c2[tex]\lambda[/tex])/h = [tex]\lambda[/tex]/[tex]\lambda[/tex]` - h/[tex]\lambda[/tex]`cos[tex]\theta[/tex]

    After some more fiddling I get to this:

    [tex]\lambda[/tex]` = h/m2c2 - (h/[tex]\lambda[/tex])(h/m2c2)cos[tex]\theta[/tex]

    It's kind of close but not really... I can write out all the steps I made if that is necessary, but I'm kind of hoping I made one nice, simple-to-fix error that is glaringly obvious to the more experienced :)

    Thank you :)
  2. jcsd
  3. Jan 19, 2009 #2


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    Science Advisor
    Homework Helper

    Hi latitude! :smile:

    (have a lambda: λ and a theta: θ and a psi: ψ :wink:)
    eugh :cry:

    the first - should be a + :wink:
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