HW12sol - 1 C:\User\Teaching\505-506\F10\HW12sol.doc PHY...

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Unformatted text preview: 1 C:\User\Teaching\505-506\F10\HW12sol.doc PHY 505 Classical Electrodynamics I Fall 2010 Homework 12 with solutions Problem 12.1 (to be graded of 30 points). Find the temporal Greens function of a medium whose complex dielectric constant is the following function of frequency: i m nq 2 ) ( 1 ) ( 2 2 2 , using (i) the Fourier transform, and (ii) the direct solution of the differential equation which describes the corresponding model. Hint : For working out the Fourier integral, you may like to use the Cauchy theorem see, e.g., MA Eq. (15.1). Solutions : (i) In class, we have derived the following relation between ( ) and G ( ) see Eq. (7.24) of the lecture notes: ) ( ) ( d e G i . ( * ) Though the actual (physical) Greens function G ( ) does not have sense at < 0, mathematically nothing prevents us from extending integral (*) to the whole axis - < < + , taking G ( ) = 0 at < 0. Now we can use the regular Fourier theorem to write the reciprocal transform: d e G i ) ( 2 1 ) ( ....
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HW12sol - 1 C:\User\Teaching\505-506\F10\HW12sol.doc PHY...

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