Question: Use the Kramers-Kronig relation (7.120) to calculate the real part of ?( w ), given the imaginary part of ?( w ) for positive w

Use the Kramers-Kronig relation (7.120) to calculate the real part of ?(w), given the imaginary part of ?(w) for positive w as

(a) Im ?/?₀ = ?[?(w ? w₁) - ?(w ? w₂)], ? ? ? ? ? ?w₂ > w₁ > 0

(b)

In each case sketch the behavior of Im ?(w) and the result for Re ?(w) as functions of w. Comment on the reasons for similarities or differences of your results as compared with the curves in figure. The step function is ?(x) = 0, x 0.

(af - w)? + yw Im ele,

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