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 fields9.6 which in practice (with optical frequencies) means nearly everything but laser light.
The equation of motion9.7 for a single damped, driven harmonically bound charged
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
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.