Suppose a slow-moving electron and a slow-moving proton are injected into a chamber, such that the two approach each other and are likely to combine to form an atom of hydrogen. How would one calculate the probable sequence of events, including likely emission of photon(s) over time? Will the resulting atom end up in ground state in a predictable sequence?
Note added later: I asked this question under the supposition that it was rather elementary. I was imagining a cold, dark box, sort of like an anechoic chamber, in which a photon might be emitted and never be heard from again, or better yet, a box surrounded by detectors which might record what was emitted and when.
I am still hoping there might be some such simplified approach. But I'm beginning to suspect I might be asking something much harder than I thought. Any comments will be appreciated.