The Quantum Beat: Principles and Applications of Atomic by F. G. Major

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It can be a microscopic oscillation on an atomic scale, or as large as an earthquake. Oscillations in any part of an extended object or medium with undefined boundaries almost always propagate as waves. If any solid object is struck with a sharp blow at some point, vibrations spread throughout the body, and waves are set up in the surrounding medium. If the medium is air, and we are within hearing range, the waves fall on our eardrums and are perceived as a loud sound, whose quality experience teaches us to differentiate according to the kind of object and the way it was struck.

In any event, in order to maintain a constant clock rate it is necessary only to regulate the amplitude of oscillation. We should note that the presence of the nonlinear term in the equation of motion puts it in a whole different class of problems: those dealing with nonlinear phenomena. One far-reaching consequence of the nonlinearity is that the solution will now contain, in addition to the oscillatory term at the fundamental frequency ω, higher harmonics starting with 3ω. We will encounter in later chapters electronic devices of great practical importance whose characteristic response to applied electric fields is nonlinear.

Thus ω0 Q= . 12 γ An equally useful result is obtained by relating Q to the rate of energy dissipation by the oscillating system. 14 dt 2 From this follows the important result that we shall have many occasions to quote in the future: U Q = ω0 d U . 15 dt Associated with the rapid change in amplitude is, as we have already indicated, a rapid change in the relative phase between the driving force and the response it causes. This interdependence between the amplitude and phase happens to be of particular importance in the classical model of optical dispersion in a medium as a manifestation of the resonant behavior of its constituent atoms to the oscillating electric field in the light wave.