What is the frequency of a photon?

During emission spectrum $$\Delta E=h\nu,$$ where $\nu$ is the frequency. All books write that it is the frequency of photon, but photon is a particle and not a wave.

More than that what this frequency actually is? Is it the frequency at which energy packets are released?

This wave and particle nature is causing conflict!

What is the meaning of frequency of photon? I mean it is a particle and not a wave and frequency is a physical quantity associated with a wave.

But photon is a particle and not a wave!!!

Not really, no. That is a simplified picture but it's not the full thing.

A better statement is that a photon is a discrete excitation of a given mode of the electromagnetic field. If that (classical) field mode is monochromatic, then the frequency of the photon will be the frequency of the mode.

Note that it is also possible to have single-photon states that do not have a well-defined frequency, which are formed by taking a quantum-mechanical superposition of states with well-defined frequencies over a range of such frequencies.

• Comments are not for extended discussion; this conversation has been moved to chat. – ACuriousMind Sep 11 '18 at 16:06

The frequency of light is a well defined concept, describing the electromagnetic spectrum . That light is a superposition of photons is also an experimental fact, as seen in this single photon double slit interference , where the interference pattern characteristic of the wave is built up one photon at a time.

In the quantum mechanical framework, the photon, as all elementary particles, has a probability to materialize at an $(x,y)$ of the screen, given by the $Ψ^*Ψ$ of its wavefunction, so the frequency must reside in the wavefunction of the photon, this is an example of the form :

Now write the complex wave function as a sum of real and imaginary parts $\overline E_T(\overline r)$ and $\overline B_T(\overline r)$, $$\overline{\psi}_T(\overline{r}, t) = 2^{-1/2}\left(\overline E_T(\overline r,t)+i \overline B_T(\overline r,t)\right)$$

The published paper is here.

Superposition means the addition of the individual complex wave functions before taking the overall $Ψ^*Ψ$, and as the E and B fields are the same as in the classical equation, the frequency of light is built up by the probability distributions of the superposed photons.

Thus the association of the classical frequency of light with the $ν$ in the definition of the energy of the photon $E=hν$ is outlined

In this link it is outlined how the classical fields emerge from the quantum field theoretical framework.

• It is important to note that the use of the Riemann-Silberstein vector as the wavefunction of a single photon, as used in this answer, is $-$ as Wikipedia puts it $-$ controversial, and even its original advocates acknowledge that it has important caveats (cf. e.g. §11 of arXiv:1211.2655) and should only be regarded as the 'best possible' alternative from a field of flawed possibilities. – Emilio Pisanty Sep 10 '18 at 17:06
• @EmilioPisanty my answer is qualitative and caveats are esoteric statements. For sure a wavefunction for the photon is necessary in the quantum mechanical frame, and for sure it should have the wherewithals to build up the classical electric and magnetic fields. ( I also tend to trust CERN web pages) Thank you for explaning.. – anna v Sep 10 '18 at 17:26
• All of quantum mechanics is 'esoteric', and the objections to the use of the Riemann-Silberstein vector are strong enough that multiple core sources will tell you outright that there simply isn't a photon wavefunction at all. I'm not against its use per se but I do think that it's a complicated object that should not be discussed without direct mention of its disadvantages. – Emilio Pisanty Sep 10 '18 at 17:34
• As for 'trusting CERN web pages' - you're not trusting CERN, you've just given a roundabout link to this arXiv preprint of this conference paper (i.e. the repository you've linked to includes all of arXiv, including its bad apples). That isn't bad, but I would suggest broadening the net to e.g. the full proceedings of that conference to find other competing interpretations. – Emilio Pisanty Sep 10 '18 at 17:41
• @EmilioPisanty it used to be featured in the documents of CERN before an overhaul, trying to include the archive link, made a mess of it :) – anna v Sep 10 '18 at 17:48