A Why does a photon have a defined frequency but is also somewhat localized?

[QuasarBoy543298]

a photon have defined frequency , but we treat it as a localized particle ,how that can be?

if i am looking at second quantisation, photons are modes of the electromagnetic field , and they are not localized at all , but we do know that photons are somewhat localized , like in the photoelectric effect for example .

so,what am i missing?

 

[Dale]

we treat it as a localized particle

This is incorrect. A photon has no position operator so it cannot be localized

 

[PeterDonis]

a photon have defined frequency

Some "photon" states do, but others don't. More precisely, some states of the quantum electromagnetic field are eigenstates of the frequency operator, but others aren't.

photons are somewhat localized , like in the photoelectric effect for example

The photoelectric effect doesn't localize anything; there are no position measurements of anything involved. The measurements are of voltage and current.

The closest thing you will get to "localization of a photon" is in an experiment like a double slit with an extremely low intensity source, so you can see individual "photons" hitting the detector screen as dots, that build up an interference pattern over time. But even that can be interpreted as localization of the atom that absorbs the photon, not the photon itself.

 

[Dale]

But even that can be interpreted as localization of the atom that absorbs the photon, not the photon itself.

I think that is key

 

[vanhees71]

Indeed. First of all one should remember that in quantum theory an exact plane-wave state (i.e., momentum eigenstate) is a "generalized state" for free particles (i.e., not confined to a cavity of finite volume). A real state must be normalizable and thus only wave packets, i.e., with finite width in the momentum distribution are true states.

A photon is a one-quantum Fock state of the (asymptotic) free electromagnetic field. It is not localizable in a very fundamental sense. In contradistinction to massive quanta a photon, as the quantum of a massless spin-1- field, has not even a position observable in the strict sense.

That doesn't matter much, because all we can observe concerning the "localization of electromagnetic radiation" are intensities. For photons that's the probability distribution to detect them at the location determined by the detector. The physical mechanism on the microscopic level behind many usually used photon detectors is the photoelectric effect, and there the location of the corresponding atom/molecule from which the electron is emitted through interaction with the em. field determines the location of the corresponding "detection event".