A The different interference patterns in the double-slit experiment

[fluidistic]

I've read on page 107 of the pdf http://citeseerx.ist.psu.edu/viewdo...C52141B?doi=10.1.1.205.6529&rep=rep1&type=pdf that

the apparatus influences the electron even without detecting it. The interference pattern we obtained by selecting the undetected electrons is not quite the same as the one obtained when no attempt is made to detect them.

. Thus it seems that there are three different interference patterns.
1: We do not try to detect the electron passing through the slits, this leads to an interference pattern, call it of type 1.
2: We try to detect the electron (by using the presence of 1 atom as apparatus, as the paper mentions), but we fail to detect it. This leads to an interference pattern, but of a different type than type 1, call it type 2.
3: We try to detect the electron and we're successful. In this case, there is no interference pattern.

My main question is, what is the difference between the interference patterns of type 1 and type 2?

What's going on with the wavefunction of the electron when we try to detect it but we fail? In that case the wavefunction does not collapse into an eigenstate I suppose, but we still modified it simply because the atom acts as a perturbator potential? Is it just as simple as that?

 

[Cthugha]

My main question is, what is the difference between the interference patterns of type 1 and type 2?

What's going on with the wavefunction of the electron when we try to detect it but we fail? In that case the wavefunction does not collapse into an eigenstate I suppose, but we still modified it simply because the atom acts as a perturbator potential? Is it just as simple as that?

Please note that something like a single distinguished shape of the interference pattern does not exist. In any double slit experiment, the pattern you will see depends on the relative phase difference of the light fields/wave functions/whatever you use at the slit. You shift the positions of the peaks around if you change the relative phase. For convenience, most of the time the pattern is shown for 0 phase difference, but this is not required at all.

Accordingly, everything that changes this relative wave function, will change the interference pattern. This may be achieved by shooting a light field at some angle to the slits or for example by placing a thick sheet of glass at one of the slits as it shifts the phase of the light field at this point. Placing an atom at the slit will introduce a similar phase shift for electrons and is basically the equivalent of the sheet of glass I described beforehand for a double slit using light.