I am a mathematician and I am studying string theory. For this purpose I studied quantum theory. After reading Feynman's book in which he described the double-slit experiment (Young's experiment) I was wondering if I send one electron per day or per month (even more), could I see the interference pattern?
Answer
Yes, the interference pattern will occur, although you'll have to wait a while to be able to see it. As long as the average arrival time between photons is markedly greater than the travel time from slit to detector, the actual rates don't matter - each photon interacts with the slits by itself.
This URL shows such an experiment, in which a laser beam was so attenuated that the separation between photons was in the kilometer range, while the target-detector distance was in the meter range, and an image intensifier was used to detect photon positions. After about 500,000 photons had been detected, the result was
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