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I read that in triple or more slits experiment, the particle can sometimes though lower probability of going through all the slits and interfere with itself many times at once? I used to think it is the distance between the gaps but now suppose repeats for a million slits versus double slit, I wonder if the classical math can still works in both case?

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  • $\begingroup$ Can you please rephrase your question? It is really hard to understand. $\endgroup$ – gented May 27 at 12:35
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    $\begingroup$ What you are describing is known as a diffraction grating $\endgroup$ – By Symmetry May 27 at 12:38
  • $\begingroup$ Even up to no screening at all (that is, taking so many slits that they finally eat up all material), the math would still work: the actual trajectory of a particle is the interference of all trajectories it could take. See path integral formulation. $\endgroup$ – Stéphane Rollandin May 27 at 12:58
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    $\begingroup$ In an experiment of electron diffraction by a crystal lattice the electron has a lot more than a million slits to "go through". $\endgroup$ – nasu May 27 at 13:12
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As @ronadin explained you can look A. ZEE QUANTUM FILE THEORY IN A NUTSHELL how putting infinite girts will lead you to path integral formulation. On a modest level you can see any book on physics optics, Ghatak or Jenkins how to deal with n holes it has to do with geometric series sum of complex phases and sin(n theta) comes.

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