Wave physics : oscillations, solitons, chaos / Stephen Nettel

It starts from the mathematical introduction, focused on Fourier analysis and generalized functions (distributions). As summary, a comparison is given between formulae governing representation in vector and Hilbert space of arbitrary vectors and functions, respectively. The second chapter presents the theory of linear oscillators. Then, linear waves are considered first on strings, next electromagnetic waves are studied in the general context of Maxwell's equations together with some topics from wave optics. The Green's function method of finding the solution for forced motion is described. The subsequent section is devoted to an explanation of the operation of oscillators in general, and then is extended to a description of an actual pendulum clock. The next step is an elementary introduction to quantum mechanics. The analysis is based on a systematic treatment of driven motion using Green's function techniques. The techniques are likewise applied to the problem of a stretched string driven from one end. In two last chapters, an elementary presentation of some aspects of the nonlinear dynamics is given – nonlinear dispersive waves on water, including the concept of the soliton and an idea of inverse scattering transform, and then dynamical chaos in classical and quantum systems is described. There are problems dealing with Einstein photoelectric effect, Huygens principle, the square aperture, gratings, Rayleigh's criterion for resolution, Debye-Scherrer X-ray diffraction, and attenuation in metals. (Zentralblatt)

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