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10. Kramers-Kronig relations. Show by explicit calculation that the linear susceptibility of an optical transition modeled in the two-level approximation obeys the Kramers-Kronig rela- tions, but that neither the total susceptibility x nor the third-order susceptibility x) obeys these relations. Explain this result by finding the location of the poles of x and of x3). [Hints: x) and x) are given by Eqs. (6.3.33) and x is given by Eq. (6.3.23).] 11. Kramers-Kronig relations. For the classical anharmonic oscillator model of Eq. (1.4.20) show by explicit calculation that x)(20;0,w) obeys the Kramers-Kronig relations in the form (1.7.12). Show also that x(W1; 63, -62) does not satisfy Kramers-Kronig relations.