# Electromagnetic wave associated with a single photon

To the question regarding the relation between the energy of a photon (E = hf) and the energy of the associated electromagnetic wave, I read somewhere that the energy of an electromagnetic wave is Nhf, N representing the number of photons per second that pass through a unit area. How could the electromagnetic wave associated with a single photon produce several photons? If I read it wrong and it isn't, how can we represent the electomagnetic wave associated with a single photon and what would be its energy as a function of its frequency. Regards

• I suspect part of your confusion is due to the wave-particle duality inherent in trying to describe a situation either in terms of (continuous function) waves or in a stream or cloud of particles. – Carl Witthoft Aug 4 '20 at 11:42
• Thank you; I think so too. – Jean-Michel Tengang Aug 4 '20 at 14:09

## 1 Answer

The energy of a single photon is $$E=hf$$ which also corresponds to an electromagnetic wave of frequency $$f$$. If the beam of light consists of multiple photons, then the total energy of the beam of light equals the number of photons in the light beam $$\times$$ the energy of a single photon: $$E_{tot}= Nhf$$. In the wave framework, this can be seen as the superpostion of all the $$N$$ electromagnetic waves of frequency $$f$$. This resulting superposition is also a wave.

So, it can be that the total electromagnetic wave consists of the superposition of $$N$$ "fundamental" electromagnetic waves. Here, the $$N$$ "fundamental" electromagnetic waves correspond to the $$N$$ photons.