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 fields11.10 which in practice (with optical frequencies) means nearly everything but laser light.
The equation of motion11.11 for a single damped, driven harmonically bound charged electron is:
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 )
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.