**Definition 0.0.1 **  The **Lorentz oscillator** is a model for the polarization of bound electrons in a solid based on a charged mass $m$ with charge $q$, density $N$, a linear restoring force and a damping coefficient $\gamma$. The position of the charge in the potential well is $x(t)$.
\[\frac{d^2x}{dt^2} + \gamma\frac{dx}{dt} + \omega_0^2x = \frac{q}{m}E(t)\]
\[P(t) = Nqx(t)\]