How does passing particles like photons through a double-slit experiment produce diffraction when *the slit itself* is in theory a wave function of the atoms it’s built of? How does a wave diffract a wave?

How does it do it? Like that.

It’s not some fundamental immutable law of waves that they can’t ever interact with other waves at all. In this case, some of the waves are charged, and therefore those waves interact with light waves.

Maybe the wave function of the slit has a much smaller wavelength than light, that’s why its wave nature is not apparent?

In quantum mechanics, things have both wave-like and particle-like characteristics, and any either-or description will fail to capture the full phenomenology. So a quantum object can diffract another quantum object just as well as a particle can diffract a wave.

Personally, though, I find it more intuitive to consider the explanation for this behaviour to be given by a modification of probability theory: the ‘probabilities’ (more accurately, the probability amplitudes) behave like waves, i.e. they can cancel out or reinforce one another, contrary to the situation in ordinary probability theory, where the law of total probability holds. Basically, this is due to the fact that probability amplitudes are complex numbers rather than reals, but this is merely a technical detail. What matters is that therefore, the probability that a photon reaches a certain point on the screen (or in space) is not given by the sum of the probabilities that it reaches that point via either one slit. Rather, the probabilities may interfere destructively, and thus, the probability that the photon reaches some point may be lower than the probability that it reaches that point via slit 1 plus the probability that it reaches that point via slit 2; and thus, interference patterns and diffraction occurs, without having to talk about whether the photon is a particle, a wave, or something else entirely.

What I was getting at was classical diffraction assumes that the hole in a barrier that a wave is passing through has infinitely sharp edges- that at any infinitesmal point in space either the wave passes through or is blocked. But if in real life there’s some quantum fuzziness at the edges (or worse, you can’t really think of the barrier and the slit as classically solid), then how does that affect diffraction? Is the interference pattern slightly different than a classical experiment due to these effects?

I believe it’ll be the same interference pattern – the pattern consists of a great many individual photons, which must be averaged over; but in this average, the edges of the slit, even if they’re considered as quantum objects, will be at the same ‘position’ as classically.