Single photon radio wave

Question

If there is a single photon representing a radio wave with wavelength say 10 m, what does this 10 m really mean? Does it mean that the photon itself could be anywhere in those 10 m?

Answer 1

No. It means that the classical plane-wave solution to Maxwell's equation has wavelength 10 meters, and that the occupation number of that mode is unity. The single photon has an equal probability of being detected anywhere in the universe.

Answer 2

The wavelength of quantum mechanical particles is in a solution of the appropriate equation,$Ψ$. The $Ψ^*Ψ$ is the probability distribution from which the probability of finding the photon at (x,y,z,t) is given.

In addition, a real photon is represented by a wave packet solution, so there will always be a width in the experimental footprints.

If the basic wavelength is 1o meters, it means that the probability of the photon interacting is within those 10 meters within the width given by the wave packet.

You ask:

But is that wave packet somehow related to the classical electromagnetic wave associated with the photon

Here one can see how in quantum field theory terms the classical electromagnetic wave emerges mathematically. It is not simple. An intuitive understanding can come by studying this experiment, which shows how single photons add up to the classical wave interference pattern. The single photons leave a dot, and the wavepacket induced probabilities enter in how this dot materializes. The accumulation of photons make up the classical light interference, and the wavepacket is only part of the detection system. One must always remember that in quantum mechanics it is probabilities that are modeled.