Electromagnetic Waves

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  • #1
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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.
 

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  • #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.
 
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What are the boundary conditions for an electromagnetic wave?
 
  • #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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