It is known that any non-sinusoidal wave can be regarded as a combination of sinusoidal waves of different frecuencies, with the ‘weight’ of the different frecuencies given by the function called Fourier transform. On the other hand, if we have an electromagnetic wave, we know that it is the combined result of many photons of different energies, and it is generally assumed that the interval of the Fourier space where Fourier transform is not zero gives us the energies of the photons in the beam, through the famous relation E=h·f where f is the frecuency and h the Plank constant.(adsbygoogle = window.adsbygoogle || []).push({});

But if we have a short pulse of radio waves rising and falling abruptly, although the main frecuency is in the radio region, the Fourier transform may have also very high frecuencies, physically impossible to assign as photon energies.

Or think in a continuous (cuasi)monocromatic wave source, a detector, and a shutter between them, which allow us to switch the wave on and off. For the source, the radiation have only one frecuency, but after the shutter, the fourier transform of the wave has also other frecuencies. However photons should have the same energy!

So ¿in which cases or under which conditions can we relate the ‘matematical’ frecuencies given by fourier analysis with photons energies?

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# 'Mathematical' frequencies and photons

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