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I'm reading on page 107 of this Van Kampen's paper 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.

which strickes me a lot. I had never read that anywhere before, and I wonder how it's possible. Then

If one wants the electron to be able to act on the measuring apparatus one cannot avoid a reaction. Yet the fact that an apparatus affects the wave function of the object system even when the measurement is not successful has caused some debate

The paper mentions "an atom" as the apparatus. So let's say we are performing the double-slit experiment with an atom at the slits that tries to detect the electrons passing nearby. The only way I know about ways to modify the wavefunction of the electrons is by introducing a potential, so that the Schrödinger equation is modified and it's almost obvious that the resulting wavefunction is altered even when the electron isn't detected. Is it that simple? I.e. is the potential term of the Schrödinger equation introduced by the atom is what modifies the wavefunction of electrons passing nearby, so that there is still the interference pattern, albeit a modified one compared to when the atom at the slits is missing?

Or is it deeper than that (involves the collapse/non collapse of the wavefunction)?

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  • $\begingroup$ Simply put : Atom introduced at any slits randomizes the phase difference between electrons amplitude to take each of the paths and hence suppresses interference. You can search for decoherence due to entanglement between system and another apparatus. Quite a good amount of work has been done on this. $\endgroup$ – Sunyam Oct 19 '17 at 22:45
  • $\begingroup$ When you mean "surpresses interference", do you mean like a binary thing, i.e. either supressed interference entirely or not entirely? Because the source I quote claims there is still interference although not exactly the same. $\endgroup$ – thermomagnetic condensed boson Oct 20 '17 at 17:26
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    $\begingroup$ I didn't mean it like binary. I meant that it reduces. I can write a detailed answer sometime, if you want. $\endgroup$ – Sunyam Oct 20 '17 at 17:28
  • $\begingroup$ Great! I'd be glad about the answer. $\endgroup$ – thermomagnetic condensed boson Oct 20 '17 at 18:06
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    $\begingroup$ @thermomagneticconensedboson I have been a bit busy right now. I realized that answering your question rigorously involves (including coming up with a simple model) involves more effort that what I thought. I hope to give an answer when i get a stretch of time. $\endgroup$ – Sunyam Apr 4 at 17:35
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This is rather a comment as an answer, but it is much too long for a comment.

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.

Which impresses me, too, but for other reasons. Usually for all deflections at edges the superposition of wave functions at different points in space is the reason for intensity distributions on an observer screen. Even for single edges with involved one by one photons or electrons the explanation follows this point of view. The particle interferes with itself.

The influence of the edge, or better the particles of the edges material is not taken in any consideration. Van Kampen introduces an electron and you are proposing

is the potential term of the Schrödinger equation introduced by the atom, what modifies the wavefunction of electrons passing nearby, so that there is still the interference pattern, albeit a modified one compared to when the atom at the slits is missing?

That is, what I’m trying to get in discussion in PSE for a while.

A photon has an altering electric field component. It should be permissible to assume that by this field some photons interacts with the electric field of the surface electrons of the slits material. This are the photons which are not hitting the wall and not going uninfluenced through.

Since both the negative and the positive value of the photons electric field are involved, some photons arrive the observation screen behind the geometrical shadow and some arrive away from this line. Not so electrons, the all get deflected (in some range of distance to the edge) due to their always negative electrical potential away from this line.

This different behavior of photons and electrons at edges should be a very important argument for the interaction of the edges field and the particles field.

How is the wavefunction of an electron affected by the presence of an atom at the slits in the double-slit experiment?

If this question could be calculated for a additional atom, it could be calculated for an electron on the edges surface too. This will disprove or prove the influence of the edges particles on the intensity distribution behind edges and slits.

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