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I know that is what most, if not all, physicists hold to be the case. However I myself would never speak of it in such terms. The reason for my position is that such a self-interference of a single particle with itself cannot be observed. It's not even clear to me what it means in practice. I know that it sounds nice and comfortable to speak of it that way but I have my reasons to disagree, and I hold that these reasons are strong. Here's my reasoning. Take a single particle and fire it at a double slit screen such as the one in Young's double slit experiment. The particle will strike the screen at one single location. In that experiment there is no evidence of a particle interfering with itself. If we have a large ensemble of identical setups there will be a pattern which emerges when we compare the results from all experiments. That does not imply that the particle interferes with itself.

I agree.

So why is there a pattern? What determines the geometry of the pattern? There's a pattern because the double slit is in reality a potential well. The shape of the potential well determines what the wave function will be.

You mean the potential is infinite on all the first screen's points excepting on the slits' points where it is zero?

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