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I know that there is a formula for the optical path difference of two light beams going through two different slits, which is given by $\Delta x= a\sin(\alpha)$ where $a$ is the distance between the slits. So we know that the phase difference is given by $ \ \frac{2 \pi}{\lambda} \Delta x$.

Now my question is: what happens if we use atoms instead of photons? Can we plug in the de Broglie wavelength into the expression for the path difference in order to get an expression for the detected intensity, in the case of general atoms? So can we use the de Broglie wavelenth and work as in the case of photons to get an expression for constructive and destructive interference?

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    $\begingroup$ I would say that you have answered your question simultaneously. Yes you are correct in your thinking $\endgroup$
    – hsinghal
    Commented Aug 4, 2016 at 17:25
  • $\begingroup$ What happens is that we build a new type of microscope: en.wikipedia.org/wiki/Scanning_helium_ion_microscope that uses helium ion beams to image samples with sub-nm resolution. Cool! :-) $\endgroup$
    – CuriousOne
    Commented Aug 5, 2016 at 3:15

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The reason that the double split effect works on photons is because of the length of their wavelength, as you say. It would not be very interesting for massive atoms, since they would not interfere with each other as in patterns of interesting interference.

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    $\begingroup$ Yet, they do in reality. $\endgroup$
    – Jon Custer
    Commented Aug 4, 2016 at 21:13

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