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Electromagnetic Waves

  1. Apr 6, 2005 #1
    From Griffiths: Problem 9.4 Obtain Eq. 9.20 directly from the wave equation, by separation of variables.

    Eq. 9.20: f(z,t)~ = integral [-inf, inf] A~(k)e^i(kz-wt) dk

    where ~ denotes the complex conjugate

    the wave equation: f''(z) = (1/v^2) f''(t)

    I'm a little confused on how I can separate the variables. Can I assume that I can represent f(z,t) as A sin(kz)cos(kvt) and then calculate the aforementioned 2nd derivatives.

    I think my reasoning is correct but my math.... well my math isn't up to par.
     
  2. jcsd
  3. Apr 6, 2005 #2

    dextercioby

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    You want to solve the the 1D linear PDE

    [tex] \frac{\partial^{2} f}{\partial z^{2}}=\frac{1}{v^{2}}\frac{\partial^{2} f}{\partial t^{2}} [/tex]

    with proper boundary conditions (field-type)...?

    Use the Fourier transform...

    Daniel.
     
  4. Apr 8, 2005 #3
    What are the boundary conditions for an electromagnetic wave?
     
  5. Apr 8, 2005 #4

    dextercioby

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    There are none.Simply the solution be writible as a Fourier series (discrete spectrum of frequencies),or as Fourier integral...

    Daniel.
     
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