The obvious generalization of the static model for the polarization is
to assume a *damped linear response* to a *harmonic* (plane
wave) driving electric field. That is, every molecule will be viewed as
a collection of damped, driven (charged) harmonic oscillators. Magnetic
and non-linear effects will be neglected. This is valid for a variety
of materials subjected to ``weak'' harmonic EM fields^{9.11} which in practice (with optical frequencies) means nearly
everything but laser light.

The equation of motion^{9.12} for a single damped, driven harmonically bound charged
electron is:

(9.111) |

(9.112) |

Actually, we have molecules/unit volume each with electrons
where of them have frequencies and damping constants
and , respectively (whew!) then (since we will stick in the
definitions
and
)

(9.113) |

(9.114) |

These equations (within suitable approximations) are valid for quantum theories, and indeed, since quantum oscillators have certain discrete frequencies, they seem to ``naturally'' be quantum mechanical.