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If we want to check experimentally that, for a photon:

λ=h/p (De Broglie equation)

  1. Has such experiment been carried out?

  2. What is/would be the experimental setup?

Wikipedia doesnt show such protocol for a photon

EDIT: my question is badly worded, De Broglie's equation for a photon would be called Planck–Einstein relation

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    $\begingroup$ Isn't the photoelectric effect itself the confirmation of the de-Broglie relation for photons? I mean, in my understanding, the photoelectric effect first established (to some extent at least) this relation for photons and de-Broglie, explicitly inspired by the photon-case, then generalized it to the rest of the particles. Correct me if I am mistaken. $\endgroup$ – Feynmans Out for Grumpy Cat May 18 at 18:39
  • $\begingroup$ @DvijMankad your answer seems correct, en.wikipedia.org/wiki/Photoelectric_effect#Stopping_potential $\endgroup$ – Manu de Hanoi May 18 at 18:58
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There are two cases:

  1. relativistic, one cannot prove the De Broglie's hypothesis, it should be a postulate.

  2. non-relativistic, it can be proven by the photoelectric effect

Now de Broglie's hypothesis was that this equation for photons (photoelectric effect) not only works for massless particles, but for massive particles as well, this is how Schrodinger got the idea.

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  • $\begingroup$ Could you elabrate on what you mean by the relativistic case ? Photons always move at relativistic speeds $\endgroup$ – Manu de Hanoi May 19 at 5:37
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A thought experiment would be to measure the radiation pressure by reflection on a surface. You could use a torsion balance, in vacuum to avoid gas flow.

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  • $\begingroup$ I think that analysis would work classically, too, though, so there is no appeal to $\hbar$. $\endgroup$ – JEB May 18 at 18:46
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    $\begingroup$ I doubt this would be accurate enough to get the momentum per photon $\endgroup$ – Manu de Hanoi May 18 at 18:50
  • $\begingroup$ @ManudeHanoi As Beth could measure the photon spin in 1935 in a similar manner it should be possible. Also I wrote thought experiment. I think it is feasible but it will take some engineering. What is your doubt based on? $\endgroup$ – my2cts May 18 at 19:07
  • $\begingroup$ @my2cts had a quick look, for such an experiement to give you the equation, you'd need to measure the momemtum for a known number of photons. However in order to know how many photons are emitted in the first place, you need De Broglie equation. So you are stuck in circular reasoning (or so it seems, it's late here) $\endgroup$ – Manu de Hanoi May 18 at 19:29
  • $\begingroup$ @ManudeHanoi Richard Beth did not worry about that in 1935. He knew the number of photons from the energy. $\endgroup$ – my2cts May 18 at 19:35

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