Exploring the Relationship Between Light Emission and Wavefunction: An Analysis

[dumpling]

Hi!
I would like to wrap my head around a relatively simple issue.
Lets say that you have an excited atom, which rests in your refernce frame.

When it emits light, the atom will have a backreaction, and it will "gain momentum" with the opposite direction as the photon.
Of course, without measurement, the photon's "wavefunction", or the spatial function of the electromagnetic mode excitation, would be spherical.

So would the wavefunction of the atom. However if we do measure position of the light, we neccesserily know which direction the atom has gone. (otherwise momentum conservation would not hold)
Is this right so far?

Does this imply that the light-atom wavefunction is a mixed state? I guess not, because the light can be diffracted.

Nevertheless my question is: How could one precisely describe the state of the whole system?
Can it be a sum of | atom one direction>|light opposite direction> ?
What would be a precise description?
Is the light alone in pure state?
is the atom alone in a pure state?

Thanks in advance.

 

[Nugatory]

How well do you understand the quantum physics of a two-electron system? If your setup involved two nearby electrons repelling one another (initially at rest in some frame, then they start moving) would you be able to answer the questions you're asking about it?

I'm asking because when we introduce photons into the problem we also introduce a tremendous amount of additional complexity. Instead of using the ordinary non-relativistic quantum mechanics that we learn in undergraduate classes, we need relativistic quantum electrodynamics. You don't want to go there until you have a solid grasp on the simpler non-relativistic problem.

 

[dumpling]

I thought I understood it, but I guess it is always useful to revise.
I understand for example what is written here: https://farside.ph.utexas.edu/teaching/qm/lectures/node96.html

Of course, actually calculating the dynamics of two interacting electrons is something i have never done, but I imagine that for a spin-singlet state, an initial spherical symmetry would not be disturbed. At least until it interacts with sensors.

Altogether I am thankful that you asked, as it made me think a bit.
I think in the end, I understand the case of two electrons in the setting that it is related to my question.
(Altough singlet state cannot be initially in a state where each electron has spherically symmetrical spatial wavefunction, if I am correct)

Also sorry for my english.

 

[dumpling]

My question still stands of course.

But then again, if the velocity of the atom, and the energies are small, and the atom does not have spin, then isn't the only relativistic component that is relevant, is the quantization of electromagnetic field?