Can Multiple Electrons in a Double Slit System Interfere With Each Other?

[PatrickPowers]

So I read that in double slit systems the intensity of the "particle" source does not matter. If it is known that only one particle is in the system at a time, the interference pattern will be the same as observed when there are multiple particles in the system. From this we can conclude that the particle is interfering with itself.

What puzzles me is this. Let;s say we have multiple electrons in the system. Shouldn't they repel one another and hence blur the interference pattern? Even if they didn't repel one another, wouldn't the phase of one electron be random with respect to the phase of any other, and this would eliminate the interference pattern except for the case of the electron interfering with itself.

So I have something wrong here. What is it?

 

[Simon Bridge]

electrons in a beam do repel each other and that does blur the image. A lot of effort goes into focussing and guiding the beam. Notice that CRT TVs are capable of quite good electron placement over meter-lengths.

the "phase" is in the quantum wavepacket not the "electron" - this is where we need to be careful about what we are talking about.

Feynman did a series of lectures on wave-particle duality and explains the relationship quite well.
http://video.google.com/videoplay?docid=1501838765715417418
... see the whole lecture series. It's worth it.