I find that I make references to this paper quite often, so I thought I might as well post it here so that it would easy for me to find. :)
We tend to point to the interference observation as an "evidence" for the wave nature of something. This is certainly true about light when we continue to describe it as having "wave-particle duality" (which, if you've read my earlier post, I don't agree with). On the other hand, if we believe that QM is also a valid description of light, then QM formalism should also describe the wave behavior that we observe. Yet, whenever we want to describe such interference, we continue to invoke the classical wave description rather than the "particle" nature of light.
Of course, the main reason why we do this is because it is a lot easier (and more transparent for most people/students) to use the wave picture. Still, QM should, in principle, be able to arrive at the same interference effect that we know and love. Most basic QM texts do not go into this, with the argument that such derivation is to complicated for that level.
So it was quite a joy to discover this paper a few years ago. Thomas Marcella has written a rather useful paper in which he explicitly used only QM formalism to derive all the interference phenomena, without invoking any classical wave picture. In it, he solved for the single, double, and multiple slits scenario. Of course, this technique can also be reformulated via Feynman's superposition of paths, but Marcella's technique is a lot more familiar with what undergraduate QM students would have seen.
A useful reference to have whenever someone argues with you that the particle/QM picture cannot describe the interference/diffraction patterns.
T.V. Marcella Eur. J. Phys. v.23, p.615 (2002). The preprint can be obtained here.