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Adapted systems of eigenfunctions for one-dimentional Helmholtz equation


R.M. Gadelshin – Ph.D. (Eng.), Associate Professor, the pulpit radio electronic and quantum devices of Kazan National Exploretory Technical University by named A.N. Tupolev

A transition from wave equation towards Helmholtz equation by method of division variables installs both a value of the wave number, and implies a presentation of the spatial distribution within the framework of its certain total description at unlimited space. Solving of the task for limited domain with provision for adherence of the last condition allows getting of the decision, that beyond the solution as alone component of known system of eigenfunctions. The possible decision in evident form is obtained for one-dimensional task, herewith turns out to be the possible generalization of the decision on events «non resonance» sizes of the domain. In this case turns out to be possible introduction some adapted towards value of the spatial frequency system of eigenfunctions. The getted decision of the one-dimensional task is used to describe a current distribution along the length of the passive vibrator, permitting a description of frequency dependency of its effective surface scattering.

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