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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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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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