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## Main Question or Discussion Point

I've read that, in general, the energy of a wave, as opposed to what's commonly taught, isn't strictly related to the square of the amplitude. It can be seen to be related to a Taylor series, where E = a

My questions are:

_{o}+ a_{1}A + a_{2}A^{2}.... Also, that the energy doesn't depend on phase, so only even terms will occur and the Taylor series gets truncated to only be proportional to the amplitude squared.My questions are:

- Is there a derivation/more in-depth explanation of how the Taylor series came about for relating energy to amplitude?
- Why doesn't energy depend on phase? (My guess is because it's based on a simple harmonic oscillator model)
- Since phase isn't important, why will the odd terms in the series not be important? How are those two things related?