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^{11.10} which in practice (with optical frequencies) means nearly
everything but laser light.

The equation of motion^{11.11} for a single damped, driven harmonically bound charged
electron is:

(11.59) |

where is the damping constant (so is the velocity dependent damping force). If we assume that the electric field and are harmonic in time at frequency (or fourier transform the equation and find its solution for a single fourier component) and neglect the transients we get: = -e = e^2m _&omega#omega; (&omega#omega;_0^2 - &omega#omega;^2 - i &omega#omega;&gamma#gamma;) for each electron

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 )

(11.60) |

where the

(11.61) |

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.