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are the following statements correct:

For Young's double slit experiment with electrons, the separation between two slits has to be smaller than the position uncertainty of the electrons. But no such limitation exists for single photon experiment.

The motivation of this question is to understand the difference between the wave nature of electrons and photons.

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You are simply mistaken about the photon case. When you say "the separation between two slits has to be smaller than the position uncertainty of the electrons" you are right, and this same limitation also applies to the single photon experiment. Otherwise there would be 'which path' information somewhere, preventing the interference effect.

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  • $\begingroup$ But the position uncertainty for photons is an undefined quantity. $\endgroup$ – Kushal Shah Mar 17 at 11:00
  • $\begingroup$ The position uncertainty for photons is a measure of the spread of the wavefunction describing the photon state. For a plane wave state it would be infinitely spread out, and for other states it is spread out by some smaller amount. In practice it is a crucial feature of the Young's slits experiments to make sure the illumination of the slits is coherent and that is the same thing as saying that the photons' position uncertainty at the slits is wider that the slit separation. $\endgroup$ – Andrew Steane Mar 17 at 12:54
  • $\begingroup$ Sounds good! So a single photon corresponds to a plane wave, right? And so it has infinite spread out. Agreed? $\endgroup$ – Kushal Shah Mar 17 at 14:57
  • $\begingroup$ That is almost right. Really you can first describe the shape of some wave, be it plane or spherical, or a wavepacket, and then assign one photon to that spread-out function (called a mode). With more photons, they could all be in the same mode, or some in one mode, some in another. $\endgroup$ – Andrew Steane Mar 17 at 15:09
  • $\begingroup$ @KushalShah real particles , not field theoretical bases, are wave packets made up of plane waves about a central wavelength hyperphysics.phy-astr.gsu.edu/hbase/Waves/wpack.html. The photon field is represented by a plane wave in all space on which creation and annihilation operators operate. $\endgroup$ – anna v Mar 17 at 15:20
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Here is a double slit experiment with single photons at a time

dbslph

In the last frame the Young interference pattern appears, so it is the same conditions of distance taken from the wavelength of the emergent light from the superposition of photons. The photons have energy E=h*nu where nu is the frequency of the light that will emerge from zillion such photons. To a frequency a wavelength can always be assigned:

On the left the footprint of photons seems random, but the probability distribution, which is the emergent interference pattern, shows that the probability amplitude of a photon being found at the (x,y) of the screen has information about the wavelength of emergent light. The modulus squared of the wave function of the photon gives the probability. How this happens needs to be studied in quantum field theory.

So it is the wavelength in both cases , of electron and photon interference, for the electron given by the de Broglie wavelength.

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  • $\begingroup$ Please respond to my comments on the 2 other responses. $\endgroup$ – Kushal Shah Mar 17 at 11:47
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There is in principle no difference between the diffraction patterns if the De Broglie wavelength of the electrons is the same as the wavelength of the photons.

There are simple formulas to describe what the interference pattern looks like depending on wavelength, slit width and slit separation. https://en.m.wikipedia.org/wiki/Double-slit_experiment.

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  • $\begingroup$ But if the slit separation is much higher than the electron position uncertainty, would not we get only a diffraction pattern since the electron probability distribution function would essentially go through one slit. $\endgroup$ – Kushal Shah Mar 17 at 11:47
  • $\begingroup$ @KushalShah For photons , too if the separation is much larger than the wavelength of its frequency (E=hnu) there will be only single slit diffraction at the projection of each slit. $\endgroup$ – anna v Mar 17 at 15:23
  • $\begingroup$ In this 2013 NJP paper on double slit email with electrons, authors report that electron de Broglie wavelength was only 50 picometers, but slit separation was 272 nanometers, clearly much larger than wavelength. iopscience.iop.org/article/10.1088/1367-2630/15/3/033018 $\endgroup$ – Kushal Shah Mar 17 at 16:13

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