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Sum over histories and double slit?

  1. Apr 21, 2012 #1
    I was recently studying Feynman's sum-over-histories approach to quantum probability. I also was reading an interesting paper on the double slit experiment. How do these two work together. Do some of the probability waves not have a out of phase partner to interfere with itself?

    On a related not, whats the difference between the proxy wave, and Feynman's probability waves.

    If the proxy wave is fictitious, how do atoms resist other atoms passing through it.

    I know this is a lengthy question but please try to answer.
     
  2. jcsd
  3. Apr 21, 2012 #2

    Matterwave

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    The easiest way to do the "sum over histories" for the 2 slit experiment, is to take the classical paths (2 of them) and just simply add up e^iS/h for the 2 different paths to get an amplitude. The probability is of course the absolute square of the amplitude. There is of course a normalizing factor, but that can be sometimes annoying to get, and I can't remember the details of that for the 2-slit experiment at this moment.
     
  4. Apr 21, 2012 #3
    And that value (absolute square of the amplitude) would be the probability of the electron going through both slits?
     
  5. Apr 21, 2012 #4

    Matterwave

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    No, the probability that the electron arrives at that spot in the detector. There is no probability for the electron "going through both slits".
     
  6. Apr 21, 2012 #5
    This still applies in the case of an interference pattern when only one electron is fired.
     
  7. Apr 21, 2012 #6

    Matterwave

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    Yes it does. You sum over both paths, but that doesn't mean the electron physically moves through both slits.
     
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