Suppose an electron makes a single transition from higher to lower energy level releasing energy. Would that energy be released in exactly one photon equal to $h\nu$? Also, is saying "one photon is released" equivalent to saying "one electromagnetic wave of $\nu$ frequency is released"?
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You could get two or three lower frequency photons but it’s gonna take billions of coherent photons to resemble a so called light wave. – Bill Alsept Jan 24 '20 at 22:17
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More than one photon can be emitted but these processes have lower probability. (Rule of thumb: A factor of $\alpha\approx 1/137$ for each extra photon.)
Talking about “one electromagnetic wave” is meaningless. An electromagnetic wave pulse with a small range of frequencies centered on $\nu$ is emitted. (The spread in frequencies depends inversely on the transition time.) The pulse has many wave crests and troughs.
G. Smith
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One way to understand it is because of the uncertainty relation between energy and time. – G. Smith Jan 24 '20 at 20:59
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1Another way to think about it is that the only wave with a single frequency is a sinusoidal wave that lasts for infinite time. The atom only radiates for a fraction of a second. To cancel out the wave at the other times, there must be other frequencies. This comes from Fourier Analysis. – G. Smith Jan 24 '20 at 21:02
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1@Sharad1 You can't count EM waves that way. We don't say that a brighter (monochromatic) source emits "more waves" than a dimmer source. We just say the wave emitted by the brighter source has a higher amplitude than the one from the dimmer source. – The Photon Jan 24 '20 at 22:38
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@The Photon Then what do we actually mean by one light wave,two X rays,etc. – Sharad1 Jan 25 '20 at 21:04
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The only meaning of “two X rays” is as in “I had an X ray last week and I’m having another one next week”. But you can say “I detected two X-ray photons.” This means two photons in a particular energy range. – G. Smith Jan 25 '20 at 22:06
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We know that the ocean is made of water molecules. We also see that ocean has waves. Now does that mean that each water molecule is a water wave?
Physically realisable EM waves are analogous to the water waves where many photons collectively behave in a manner where EM waves emerge. But what is astonishingly peculiar about photons is that the energy of the individual photons somehow manifests itself as the frequency of the collective that is the EM wave!
And the reason why this happens can be read here.
Superfast Jellyfish
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It's not correct to say that an EM wave is made of many photons. Even just one photon of the EM field propagates as a wave. The coherent state is the entity that comprises many photons. The confusion here is that the coherent state is the quantum state that most closely resembles a classical EM wave, a wave with recognizable amplitude and phase. The one-photon state is still a wave, but it is a peculiar one. For example, if you know its amplitude you cannot know its phase. The linked answer is good, however. – garyp Jan 31 '20 at 11:30
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I believe when the OP says EM wave they mean a physically realisable wave with oscillations in real space. The one-photon wave is a wave in Hilbert Space. – Superfast Jellyfish Jan 31 '20 at 11:33
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Perhaps, and perhaps you addressed his question. But the answer needs clarification for others who might interpret the question and answer differently. – garyp Jan 31 '20 at 11:44
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