Unformatted text preview: explain why.] 9.3H Electromagnetic waves propagating in a medium with dielectric ε (x) satisfy the wave equation ε (x) ∂ 2 ψ / ∂ t 2 = c 2 ∂ 2 ψ / ∂ x 2 , ψ = ψ (x,t). Suppose ε (x) = (1 + x 2 /2L 2 ) 2 . The medium is disturbed at x=0 by an antenna with frequency ω . If ω L/c >> 1, find the WKB solution for x > 0 for waves propagating to the right, correct to 1 st order. By demanding that |k 1 | << |k |, obtain the condition that the WKB solution is a good approximation. At what x/L do you find the worst violation? Make a sketch of the real part of ψ , to first order, over a scale of length a few L’s. Find x(t), the location of the wavepacket moving with the local group velocity if x(0) = 0. From the constancy of ω , find k(t)....
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- Fall '11
- mechanics, WKB solution, perturbative methods