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)?