I would like to see experimental results for repeated measurement of a single-particle, quantum system that is approximately either particle-in-a-box or simple harmonic oscillator. If particle-in-a-box, then ideally in a limit that is approximately "infinite" square well. Can someone point me to such results, ideally with a reference to a paper?

In response to feedback in the comments that seem to have misinterpreted the question while also, helpfully, suggesting that some context might narrow scope, here's some context for the question:

  • From theory we expect that each measurement will cause the wavefunction to collapse. It will then evolve according to the Schrodinger equation until the next measurement, when it will collapse again.
  • In theory if we push the measurements closer and closer together in time, we expect to find the particle in approximately the same place each time due to the collapse of the wavefunction from the prior measurement, which, if the measurements are sufficiently frequent, will not have much time to spread before the next measurement.
  • In theory, we also tend to assume that the measurement is instantaneous and of potentially infinite precision, whereas in practice neither is true: The measurement will take finite time to complete and have finite spatial precision.
  • Experimental results may be subject to both quantum uncertainties (due to the method of measurement itself being subject to quantum effects) and classical uncertainties, which presumably have different impact on how the wavefunction collapses.
  • Ensemble experiments, while useful, do not directly probe these aspects of quantum measurement because they typically have the "collapse" but then no direct measurement of the subsequent "evolve" and "collapse" that you'd have in repeated measurements of a specific particle.

I'm interested in experimental data that probes a system subject to repeated measurement and how that empirically does (or doesn't, if that's the case) match expectations from the ad-hoc theoretical procedure of repeated cycles of collapsing and evolving the wavefunction, especially in presence of finite-precision measurements.

Within that context, I'm trying to keep the question open-ended enough to avoid eliminating "closely" related experimental results but not completely open.

Examples of desired characteristics of a relevant experiment:

  • Takes multiple (finite-precision) position measurements of the same particle repeatedly over time.
  • Is a quantum system that is "approximately" particle-in-a-box or simple harmonic oscillator.
  • Constitutes an experimental measurement.
  • May be, but doesn't need to be, in multiple dimensions, e.g., it doesn't need to be a one-dimensional box.

Examples of things that are not of interest at this point:

  • Theoretical discussion of the Schrodinger equation in general or in the specific cases of the problems identified.
  • Theoretical discussion of quantum measurement, including collapse of wave functions.
  • Experimental results for systems that are not approximately particle-in-a-box or simple harmonic oscillator, including but not limited to discussion of the two-slit experiment or atomic orbitals.
  • Experimental measurements of ensembles rather than repeated measurements of a specific, single-particle system. (This also eliminates the two-slit experiment since each particle hitting the screen is a different particle.)

Examples of questions that are similar but that do not meet the specifications above:

Restating the question from the first paragraph, what experimental results exist within the constraints listed above, ideally with a reference to a paper?

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    $\begingroup$ To be frank, this is much too broad for this site. Position measurements are extremely tricky things to implement, because they must always (in the real world) be done with finite precision, and that has significant effects on the fundamental quantum mechanics of the description ─ and your question completely ignores those aspects. $\endgroup$ – Emilio Pisanty Aug 8 '19 at 15:05
  • $\begingroup$ @EmilioPisanty Whether or not too broad is up to the community. The last part of your comment I think is a misunderstanding. I'm interested in this question precisely because of the finite precision aspects of a real measurement. I'm open to revising the question to bring that out if you have a suggestion. $\endgroup$ – Brick Aug 8 '19 at 15:08
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    $\begingroup$ Saying "it's up to the community" is kind of disingenuous, given that voting to close is suspended while the bounty is in place. I for one would vote to close as Too Broad ─ with the rest being up to the review queue to decide. $\endgroup$ – Emilio Pisanty Aug 8 '19 at 15:11
  • $\begingroup$ As far as finite precision goes ─ there is nothing in the current text that even gets close to that, and when the text is read as written it is directly asking for experimental instances of an unphysical procedure (position measurement with infinite precision). I think that the lack of explicit handling of exactly what aspects of QM you're looking to see demonstrated in the experiment directly (and fatally) harms your question's ability to get you the answers you want, and fixing those problems would be much more helpful than throwing rep at it. But you're obviously free to disregard feedback. $\endgroup$ – Emilio Pisanty Aug 8 '19 at 15:15
  • $\begingroup$ This is the first feedback received, and I'm trying to understand and address it constructively. (The question has been open for a month.) I don't see where you read "infinite precision" into the text of the question though, so that's where I'm having problems addressing it. "Takes multiple position measurements of the same particle repeatedly over time." I don't see where that implies anything about the precision. (In any case it was not intended to imply infinite precision. A credible experiment would have some estimate of the precision in the method used.) @EmilioPisanty $\endgroup$ – Brick Aug 8 '19 at 15:18

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