By solving the non-relativistic Abraham-Lorentz (AL) equation, I demonstratethat AL equation of motion is not suited for treating the Lorentz atom, becausea steady-state solution does not exist. The AL equation serves as a tool,however, for deducing appropriate parameters $\Omega,\Gamma$ to be used withthe equation of forced oscillations in modelling the Lorentz atom. The electricpolarizability, which many authors "derived" from AL equation in recent years,is found to violate Kramers-Kronig relations rendering obsolete the extractedphoton-absorption rate, for example. Fortunately, errors turn out to be smallquantitatively, as long as light frequency $\omega$ is neither too close to nortoo far from resonance frequency $\Omega$. Polarizability and absorption crosssection are derived for the Lorentz atom by purely classical reasoning andshown to agree with quantum-mechanical calculations of the same quantities. Inparticular, oscillator parameters $\Omega,\,\Gamma$ deduced by treating theatom as a quantum oscillator are found equivalent to those derived fromclassical AL equation. The instructive comparison provides a deep insight intounderstanding the great success of Lorentz's model which was suggested longbefore the advent of quantum theory.
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