How exactly does wavefunction of an electron change when it ceases being part of an atom?

Question

This is a followup of How are electrons really moving in an atom?

As it happens, reading answers to that question I, instead of understanding more, lost some of my previous understanding.

Particularly, one of the answers contains this famous picture of a bubble chamber experiment

showing an electron hit off a nucleus, presumably by some cosmic ray or something.

So before this happened, the wavefunction of that electron was most likely the sum of very few spherical harmonics centered at the nucleus of its atom. After the event, it became something entirely different - a wave packet localized at a much smaller region, and moving quasiclassically inwards along the spiral depicted until reaching its center, where it presumably becomes recaptured in another atom ionizing it and turning into few spherical harmonics again (?)

I acknowledge that this process is well understood, maybe even described by explicitly known equations. Is it possible to describe in words the mechanism of this process? What kind of formalism describes such a drastic metamorphosis of the wave function? Presumably something which is "more wave than particle" somehow interacts with something which is "more particle than wave", as a result itself transforming into "more particle than wave". Can one give a qualitative description of what happens in this wave + particle $\to$ particle + particle kind of transformation?

Are there examples of other combinations, like wave + wave $\to$ wave + particle, or particle + particle $\to$ wave + particle, or particle + particle $\to$ wave + wave, etc.?

Answer 1

There are several misunderstandings in your question

you state:

showing an electron hit off a nucleus, presumably by some cosmic ray or something.

the electron was hit off a hydrogen atom ( it is a hydrogen bubble chamber) by the K-, the beam particle from which the electron path starts.

So before this happened, the wavefunction of that electron was most likely the sum of very few spherical harmonics centered at the nucleus of its atom.

Not correct. The hydrogen atom had a wavefunction described by a hydrogen atom wavefunction.,These are specific functions if you take the trouble to read the link provided.

After the event, it became something entirely different

After the interaction with the K-, the hydrogen atom became a proton(ion), and an electron was freed. The proton is not seen because it has a mass much larger than the electron, and with the same momentum the electron will have much higher velocity, the proton's velocity is too small for it to create a helix in the liquid hydrogen.

• a wave packet localized at a much smaller region,

no, it is an elementary particle described in QFT as propagating with creation and annihilation operators, it could be described mathematically as a wavepacket though.

and moving quasiclassically inwards along the spiral depicted

Not quazi classically, completely classically as the track obeys classical equations. That is why we talk of the particle electron.

until reaching its center, where it presumably becomes recaptured in another atom ionizing it and turning into few spherical harmonics again (?)

If the electron it is captured into a negative hydrogen ion, the whole ion will be described by a wavefunction analogous to the ones in the link above. Spherical harmonics are your vocabulary, and in any case the description is of the atom, the ion as a whole quantum mechanical entity.