Alright, sorry for that, I'll try to explain it as clearly as possible.
My question arises from why there is such an intrinsic relationship with harmonics in physics, not only in terms of the mathematics we use to describe the world in a simple way for us, but it also seems that there are phenomena in nature that correspond with this frequency.
I'll start with the doubt related to mathematics, which might justify why nature inherently relates to harmonic frequencies.
Is there another basis of periodic functions besides sin(kx), cosine(kx), or e^ikx that can generate the entire space of functions? If the only one is that (harmonic waves), then here my doubts end, but if there are more, it doesn't make sense to me that the phenomena described next correspond with the harmonic frequency instead of frequencies from other bases. From what I've read so far, I understand that more bases can exist.
Regarding the physical phenomena I'm talking about, they include, among others:
- E=h*f, the energy of a photon depends on the frequency of the associated harmonic wave, rather than the frequency of any other base.
- In black body radiation, Planck discovered that there are oscillators of energy h*f (as appears in the black body radiation formula).
- The color interpreted by our eyes also depends on the <<harmonic>> frequency of the light we see, not on the frequencies of the wave's decomposition into another base of periodic waves of different frequencies.
- The energy of a harmonic oscillator, again, is quantified in quanta h*w (again, harmonic frequency).
- De Broglie wavelength refers to the length of a harmonic (sinusoidal) wave, not any other.
- For example, in electron microscopy, to distinguish something very small, a wavelength very close to the size of the object to be observed must be used, but this wavelength depends on the harmonic frequency of the wave. This is related to edge diffraction, where the same thing happens, or in a slit, where a wave's diffraction upon passing through it depends on its <<harmonic>> frequency. That is, the refraction of a wave depends on its frequency (again, its frequency in a harmonic decomposition, if there are several, its behavior will be the sum of the behaviors for each frequency).
And probably many more cases like this can be cited.
If you don't know why, please don't divert the question to other things. In fact, I would appreciate it if you could indicate that you don't know either, so maybe more people will see it, and we might get an answer from someone who does know. This is not meant to be confrontational, but that's why this thread has stretched so long. I've asked physics degree professors and they have not been able to answer my doubt. That's why I don't think it's a simple question at all, and strangely, it surprises me that no one else wonders the same as me, just assuming that it is so and that's it.
Thank you very much, let's see if we can get a satisfactory answer.