The classical atomic model

We have seen in the previous chapter that the motion of electrons within an atom can only be correctly described by the methods of quantum mechanics. However it is often instructive to consider in detail a classical model of an atom since  

Indeed, during the early years of the twentieth century, the predictions of the classical Lorentz theory provided a guide to the development of a complete and rigorous quantum theory of the interaction of atoms and radiation. 

We now calculate the rate at which an excited atom radiates energy. We assume, for the sake of simplicity, that it contains a single electron which is oscillating harmonically with amplitude Zg and angular frequency oj along the direction of the z-axis  

The instantaneous electric dipole moment of the atom is given by 

The emitted radiation is linearly polarized in the plane containing tlie z-axis and the point of observation, P. The time-averaged intensity at P is given by the Poynting vector, equation (2.46)  

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The radiation reaction force. We return to a consideration of the classical atomic model which was introduced in sections 4.1 and 4.2. We found that there was a loss of energy in the form of radiation which occurred slow ly over many cycles of the electron s motion. However, this loss of energy was not taken into account in the mechanical equation of motion of the electron. This situation can be remedied by introducing a radiation reaction force, F, such that the work done by the reaction force in one cycle of the oscillation is equal to the energy emitted into the radiation field ... 

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