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