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From the Wikipedia page on single photon sources:

The Heisenberg uncertainty principle dictates that a state with an exact number of photons of a single frequency cannot be created. However, Fock states (or number states) can be studied for a system where the electric field amplitude is distributed over a narrow bandwidth.

I know that there is:

  1. Energy-time uncertainty

  2. Momentum-position uncertainty

  3. A consequence to 1 and 2, count-phase uncertainty meaning a single photon’s timing(or location) cannot be defined simultaneously. A further consequence is no definite E or B field for a single photon.

But is it true that a single photon of a single frequency cannot be created, only a single photon of narrow frequency range? How can one show this is true?

nemui
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    That is not what the quote you give says" dictates that a state with an exact number of photons of a single frequency" It is talking of ensembles of photons. – anna v Mar 15 '22 at 13:18
  • Thanks! yes I made some errors in my question, hopefully the overall question stands. Related:Here is a paper on (uva near blue)355-nm-wavelength single photon double slit experiment. https://aapt.scitation.org/doi/full/10.1119/1.4955173 – nemui Mar 15 '22 at 13:38
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    maybe this answer of mine helps https://physics.stackexchange.com/questions/689659/is-a-single-photon-a-wave-plane-or-a-wave-packet/689703#689703 – anna v Mar 15 '22 at 13:59
  • Thanks ps:the Wikipedia quote seems to conflate Electric field with the frequency of a single photon, I think these are not the same, the frequency of a single photon is the d/dt of the action ie. how the probability of a single photon being emitted is changing with time, vs an EM field which is the sum of many photons. I think so far the answer is yes you can have a definite energy single photon but I might be wrong. – nemui Mar 15 '22 at 14:12
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    Yes, hν within measurement errors in ν the ensemble of the zillions of photons that make up the classical light, in the single photon you linked.(ν from the interference pattern). It ends up on how monochromatic the laser is. – anna v Mar 15 '22 at 15:17
  • @annav I notice with some humor that your referenced answer includes a reference to yet another answer of yours! – Carl Witthoft Mar 15 '22 at 15:20
  • @CarlWitthoft I an tired of writing the same things over and over – anna v Mar 15 '22 at 15:34
  • @CarlWitthoft Thanks yes the answer is consistent with my view that a single photon can have a definite energy just not a definite location.. As does the experimwnt I linked (definite E=hf for single photon rrsultung in expected interference pattern sending individual photons one at a time). – nemui Mar 15 '22 at 15:42

1 Answers1

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If you assume that a photon is associated with an electromagnetic wave packet of finite size, then Fourier analysis tells us that it can be characterized as a combination of longer waves with a range of frequencies (and an uncertain energy). If the packet is very long then the energy (and momentum) become more sharply defined, but then you cannot predict with accuracy where or when it will interact with something else.

R.W. Bird
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