Sum over histories and double slit?

[beatlemaniacj]

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, what's 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.

 

[Matterwave]

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.

 

[beatlemaniacj]

And that value (absolute square of the amplitude) would be the probability of the electron going through both slits?

 

[Matterwave]

No, the probability that the electron arrives at that spot in the detector. There is no probability for the electron "going through both slits".

 

[beatlemaniacj]

This still applies in the case of an interference pattern when only one electron is fired.

 

[Matterwave]

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