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As explained in the answer to a question In the double slit experiment, using only one photon, will it create a diffraction pattern on an ultra sensitive screen?

During its path from the light source through the slits to the screen the light is delocalised, that is the photon doesn't have a position in the sense that macroscopic objects have a position. That's why it is able to pass through both slits at the same time.

Such an explanation couldn't explain fringes from single photons (over time) behind single edges. What is the explanation for the phenomenon that single photons produce fringes even behind single edges?

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HolgerFiedler
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    Why doesn't this explanation work? – Peter Shor Apr 11 '17 at 16:44
  • @Peter "the photon is delocalised" how nearby the edge? And at which distance to the observers screen it is localised again? Usually it is pointed out that the two slits are responsible for the interference. How the interference occurs for single photon in the interaction with a single edge? – HolgerFiedler Apr 11 '17 at 16:50
  • First, you should understand why classical waves undergo diffraction patterns when going around a single edge. – Peter Shor Apr 11 '17 at 16:55
  • @Peter Could you answer my question in the comment, please? – HolgerFiedler Apr 11 '17 at 16:58
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    The same explanation as for every other diffractive effect: Huygens' principle. No, really. You seem to really have a bee in your bonnet about this, but are simply ignoring that it is the same as every other diffractive interference experiment. See https://en.wikipedia.org/wiki/Knife-edge_effect. – dmckee --- ex-moderator kitten Apr 11 '17 at 16:59
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    @dmckee this explains the diffraction (bending) behind edges but not interference (fringes). – HolgerFiedler Apr 11 '17 at 17:04
  • No. It explains the fringes, too, because the wavelets interfere with one another. If that's not clear, you simply need to sit down and do the math. Mind you, for the knife-edge the math is harder than the ultra-simplified version that is presented to school kids for the two-slit experiment, but it expresses exactly the same physical principle. – dmckee --- ex-moderator kitten Apr 11 '17 at 17:07
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    @dmckee Please give a reference or better an animation for the interference behind a single edge. This is the main question I asked! – HolgerFiedler Apr 11 '17 at 17:09
  • For a reference see any text on optics (I have Fowles' Introduction to Modern Optics on my shelf which is nice because of Dover's price structure) or, say, chapter 9 of Jackson. As for "or better an animation" all I can say is: "No. You need the math." There are a variety of hand-wavy ways to deduce the rough shape of the calculation, but they rely on you're being able to understand the contribution of a path in terms of phasors. – dmckee --- ex-moderator kitten Apr 11 '17 at 17:29
  • @HolgerFiedler Did you ever find a satisfactory answer to this question? – Bill Alsept Feb 17 '22 at 06:15
  • @BillAlsept Yes, there are alternative views https://physics.stackexchange.com/a/639466 – HolgerFiedler Feb 17 '22 at 18:03

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There are two different, yet completely equivalent, ways that I look at this problem.

The first, as noted in the comments and in many other places, is to us Huygen's principle. Why does Huygen's principle work? Because the assumed incident wave function is a plane wave. Huygen's principle is one way to create a plane wave, and then select what parts of it continue to propagate. The math then gives the diffraction pattern in a straightforward way.

The second equivalent way is to again start with an incident plane wave. By Fourier transform, this means that the transverse momentum of the wave function contains all frequency components. The slits, or half edge, or whatever else is in the way then serves as a frequency filter, only letting through the frequency components that correspond to the Fourier transform of their shape. Apply that filter in momentum space, and transform back to position space, and it all works out the same.

Now, the second method is more general, since you don't have to start with an ideal plane wave, but can instead model actual sources - you just have to do the FT, apply the transverse momentum filter, and transform back.

As an aside, thinking in terms of transverse momenta also makes looking at diffraction gratings, diffraction patterns in crystals, and many other similar problems much easier. Just be careful - nobody can hear you scream in reciprocal space...

Jon Custer
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  • Jon, Huygens principle explain the diffraction (bending) of wave behind an obstacle but not the interference of what(?)ever behind an edge. Please give a reference for interference behind single edges. – HolgerFiedler Apr 11 '17 at 18:40
  • @HolgerFiedler - Hyugen's principle is a mathematical construction of a plane wave. As noted, it is mathematically equivalent to using Fourier transforms, so I'm afraid you need to justify why the math doesn't work in your particular case, yet works in all other cases. – Jon Custer Apr 11 '17 at 18:43