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passive_fist comments on Open thread, August 5-11, 2013 - Less Wrong Discussion
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This is pretty much correct, but to be more general and not just restrict yourself to the position basis, you can talk about the wavefunction in general, in terms of the eigenvector basis.
Two states 'strongly interact' if they share many of their high-amplitude eigenvectors. This is because eigenvectors evolve independently, and so if you have two states that do not share many eigenvectors, they will also evolve independently.
In the position basis, this winds up being much the same as having particles far from each other. In the momentum basis, it's less intuitive. You can have states with very similar representations in this basis but nevertheless very different eigenvector expansions.
I must admit I have very little understanding of how eigenvectors fit in with QM. I'll have to read up more on that, thanks for pointing out holes in my knowledge (though in the domain of QM, there are a lot of holes).