Problems Connected with Discrete Spectra
When a vibration is created in a finite structure, its energy may be divided into a set of well-defined vibrations that are called modes of the system. The mathematical model is usually the spectral problem of a linear operator. The modes are then associated with eigenvalues and eigenfunctions (e.g., vibrating strings, etc.). A “continuous extension” of these problems is observed in scattering studies (see chapter II). There are linear operators showing a discrete spectrum, a continuous spectrum, and an exceptional spectrum; and there are also nonlinear systems exhibiting a generalized discrete spectrum. However, we shall stay with the “generic” (most simple) cases and their relations to quantum inverse scattering.
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