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DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com. Mathematical physics is the mathematically rigorous study of the foundations of physics, and the application of advanced mathematical methods to problems in physics. Examples include partial differential equations (PDEs), variational calculus, functional analysis, and potential theory.

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Standing Spherical Wave normalization after decomposition in Plane Waves

I'm stuck in the following problem, which I tried to outline in the title. For starting, consider a spherical cavity with its oscillation modes (Spherical Bessel functions and Spherical Harmonics). …