1 Electron, 2 Slits, and the Rest of the Pattern

[Meta.Joe]

In the two-slit experiment, as I understand it, an interference pattern can be generated by sending many electrons (or photons) through the two slits one at a time, and the pattern itself gets built up over time. The explanation is usually this: A single electron travels as a wave and so interferes with itself as it passes through the two slits, and the interference pattern results from multiple electrons interfering with themselves as they pass through the two slits. My question is this: If a single wave were to pass through the two slits and interfere with itself, isn't the middle of the detector screen the only place you get constructive interference? If so, then multiple electrons, shot one at a time, should generate a pattern that exhibits constructive interference only in the middle of the screen. So, what explains the other cases of constructive interference observed across the detector screen?

 

[DrChinese]

My question is this: If a single wave were to pass through the two slits and interfere with itself, isn't the middle of the detector screen the only place you get constructive interference? If so, then multiple electrons, shot one at a time, should generate a pattern that exhibits constructive interference only in the middle of the screen. So, what explains the other cases of constructive interference observed across the detector screen?

Welcome to PhysicsForums, Meta.Joe!

There are areas of both constructive and destructive interference. They do not form the pattern you describe. If there were no interference, you would see 2 bars. With interference, there are alternating bands of constructive/destructive interference and some particles will end up far from the middle area.

http://dev.physicslab.org/asp/applets/doubleslit/default.asp

http://en.wikipedia.org/wiki/Photon_dynamics_in_the_double-slit_experiment

 

[Meta.Joe]

Thanks, Dr. Chinese! I'm glad to have discovered the forum. My question was a little unclear. I should have asked, Why don't we get the pattern that I describe, specifically when we shoot only one electron at a time through the two slits? What is puzzling me is that the multiple bands of constructive (and destructive) interference seem to require one wave's interfering both with itself and with the waves behind it. But since we are shooting only one electron at a time, there are no waves behind the electron for it to interfere with. So the the interference pattern should (it seems to me) be that of just one wave interfering with itself, which (I think) would give the pattern I have described. I just don't understand why we don't get the pattern I have described (rather than the pattern we do get) when shooting electrons one at a time. Does that make sense?

 

[DrChinese]

Thanks, Dr. Chinese! I'm glad to have discovered the forum. My question was a little unclear. I should have asked, Why don't we get the pattern that I describe, specifically when we shoot only one electron at a time through the two slits? What is puzzling me is that the multiple bands of constructive (and destructive) interference seem to require one wave's interfering both with itself and with the waves behind it. But since we are shooting only one electron at a time, there are no waves behind the electron for it to interfere with. So the the interference pattern should (it seems to me) be that of just one wave interfering with itself, which (I think) would give the pattern I have described. I just don't understand why we don't get the pattern I have described (rather than the pattern we do get) when shooting electrons one at a time. Does that make sense?

Well, a bit difficult to answer more deeply other than to say: add the 2 waves where they overlap on the screen and that is the pattern you get. This may help:

http://www.hitachi.com/rd/research/em/doubleslit.html

Here is a very technical treatment:

http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

 

[Meta.Joe]

Thanks! Technical indeed. It does seem, though, that we can get a multi-band interference pattern from just two waves interacting. Thanks again.

 

[dabble]