Re:A semi educated question... (Score 1)

The result of this solution is a set of probability functions describing the likely locations of the outbound electrons within the calculated domain. The approximation used (limiting the calculation domain with an arbitrary boundary) is most likely done by describing the areas outside of the boundary in terms of the probability wave approaching the boundary (once the electrons are far enough from the proton, treat it as a QED two electron problem) and remove the region outside the boundary from the calculation domain.

The result of this hack is an arbitrarily close approximation of the actual electron probability functions. In QED, you don't generally look for an exact prediction of the electron's location. Most of the time you are looking for a usefully accurate model. The breakthrough is finding a way to make the problem computationally tractable (which is done by the "large distance" approximation). Finding a way to calculate the large distance in terms of the near distance in all cases is the big deal here.

There are two difficulties with any Newtonian three body model (where gravity is the dominant force). The first is gathering complete information (where are all of the interacting objects). The second is computer errors including the position rounding error (at 32 bits, or whatever) and the sampling error (how often does the computer recalculate *all* of the vectors based on updated positions?). Ballistic models that describe interacting particles in terms of probability functions can be much more successful, but run into difficulty during interpretation (the electron really can be in five different places, the spaceship cannot).

By reducing distant bodies to planar gravity fields (large distance approximation), we end up with spacecraft like the Galileo probe that made it to Jupiter with only a few small course corrections to make up for the slight inaccuracies in the approximated model. But beware, it's still just a useful model. Don't expect to hit the center ring halfway across the solar system with your eyes closed based on any model. You'll need to correct (or update) your model with empirical data to make it actually work.

So, to finally answer your question. The breakthrough is going the other way (from Newtonian three body to QED). Before this, however, the QED models didn't have any way to reduce the large distance wave functions to a useful approximation. Now they do. If the large distance approximation used can be applied or extended to more complex interactions, our models of quantum interactions will be dramatically improved and our ability to describe complex probabilistic events will become correspondingly more confident.

Regards, Ross