Standing Waves and Separation of Variables
Standing Waves and Separation of Variables
复制标题
驻波和变量分离
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
M. Epstein
中科院分区：
文献类型：
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作者：
M. Epstein
尽管仅限于某些类型的偏微分方程的解决方案，分离变量的方法往往提供了一个途径的方法来解决大类的问题，并提供重要的物理见解。工程振动问题的分析提供了一个这样的例子。在这种情况下，变量的分离导致将双曲问题分解为一系列椭圆问题。同样的思想将在另一章中以类似的方式应用于求解抛物方程。该方法的主要副产品之一是作为系统的自然签名的自然属性的通常离散谱的出现。这一特性在从音乐声学到量子力学的各种应用中尤其明显。
In spite of being limited to the solution of only certain types of PDEs, the method of separation of variables provides often an avenue of approach to large classes of problems and affords important physical insights. An example of this kind is provided by the analysis of vibration problems in Engineering. The separation of variables in this case results in the resolution of a hyperbolic problem into a series of elliptic problems. The same idea will be applied in another chapter to resolve a parabolic equation in a similar manner. One of the main by-products of the method is the appearance of a usually discrete spectrum of natural properties acting as a natural signature of the system. This feature is particularly manifest in diverse applications, from musical acoustics to Quantum Mechanics.