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If I understand correctly the literature on dispersion, the atom is modeled as an electron bound to an atom by a spring with the electron behaving as a driven, damped oscillator. The electron oscillates at the same frequency as the incident electric field. However, I fail to understand how to reconcile this classical model of the atom with it quantum counterpart which describes atoms as only vibrating at certain frequencies corresponding to certain energies. Is it that most materials contain so many atoms that the frequencies over which the atoms may vibrate are essentially continuous? If so, why then the discussion of specific resonant frequencies in the dispersion literature?

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All driven harmonic oscillators, whatever their resonant frequency, and whether classical or quantum, vibrate at the frequency of the driving field. What happens as the driving frequency approaches the resonanant frequency is the the vibration amplitude gets large. In the case of a quantum atom there are a number of discrete resonant frequencies corresponding to the difference in allowed energies. When the driving frequency gets close to one of these resonances then the probablity of at transition from one state to the other gets closer to unity and the refractive index of a material made of these atoms varies rapidly.

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  • $\begingroup$ Thank you very much for your response. If a quantum atom can oscillate at any frequency can it radiate all frequencies? $\endgroup$
    – Vinny
    Commented Aug 17, 2019 at 22:06
  • $\begingroup$ @Vinny: It can scatter light at all frequencies. This for example is why the sky is blue. Light of all frequencies scatters off the air molecules --- although blue light scatters more strongly. It's hard to see individual spectral lines in the light from the sky. $\endgroup$
    – mike stone
    Commented Aug 17, 2019 at 22:12
  • $\begingroup$ Does the scattering occur with different probabilities for different frequencies? $\endgroup$
    – Vinny
    Commented Aug 18, 2019 at 0:47
  • $\begingroup$ That's what I said: blue scatters more strongly in Rayleigh scattering, so the sky is blue.... that's not because of a resonance of course, but when you are close to resonance you get stronger scattering $\endgroup$
    – mike stone
    Commented Aug 18, 2019 at 12:55

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