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Wave equation

  1. Nov 29, 2008 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations


    3. The attempt at a solution

    I don't understand how they're gone from (4) to (5) after making that substitution for U_o the [tex]k^2U_0[/tex] term becomes a derivative why?
  2. jcsd
  3. Nov 29, 2008 #2


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    If [itex]U_0(r,z)=V(r,z)e^{ikz}[/itex], then:

    [tex]\frac{\partial U_0}{\partial z}=\frac{\partial V}{\partial z}e^{ikz}+ikVe^{ikz}[/tex]

    due to the product rule.

    so.... [tex]\frac{\partial^2 U_0}{\partial z^2}=\ldots[/tex]??? :wink:
  4. Nov 29, 2008 #3
    Oops, I see now I was looking past the obvious. I'll do the calculation in the morning. Is there a reason why they leave out the [tex]e^{ikz}[/tex] from the final equation?


    edit: [tex] V = V(r,z)e^{ikz} [/tex]?
    Last edited: Nov 29, 2008
  5. Nov 30, 2008 #4


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    They haven't "left it out"...To see what becomes of that term, work out the derivatives in equation (4) using the assumed form of U_0.

    Huh?! :confused:...What are you trying to ask here?
  6. Nov 30, 2008 #5
    Worked that out now, must learn not to try and do derivatives in my head while tired.
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