# Quantum Collapse during the Measurement of the spectrum of hydrogen [closed]

We have hydrogen inside a tube, and we induce a voltage on it; a current passes through it and light is emitted. The frequencies of light correspond to the differences of the eigenvalues of the energy operator, which is the observable in question, so it is customary to give a heuristic explanation that the electric energy produced an energy transition and the residual energy was emitted as light.

At what precise moment did the wave function collapse in this experiment, if we try to describe according to the Copenhagen interpretation? How does that description work in this case? Can you maybe direct me to a paper that describes this in detail?

Some more words to clarify these questions: I would like to understand if the wave function is supposed to collapse the moment the voltage is applied, or the moment the electronic transition happens, or the moment the light arrives at the spectrometer, or the moment it hits the photographic film. It would be interesting to know what event, in that interpretation, triggers the collapse. A worked-out model of the whole situation, explaining how one describes each component of the system, would be most welcome.

Edit: This post has been marked as needing more focus, I think by people that did not understand the point of the question, to whom I'm nonetheless very grateful for their feedback (but please if you're one of them, kindly explain better what's going on because I also don't understand your position).

The question was phrased as a bunch of different questions in an effort to clarify it, but it boils down to this: what exactly is the role of quantum collapse in the standard quantum theory's description of hydrogen atom gas radiating in a tube? Thanks again.

Wave collapse happens objectively only in so-called "objective collapse theories".

In standard quantum theory, wave function collapse is not some objective process, it is a rule we use to update our psi function/density matrix when we find the real system state deviates from the state predicted by the time-dependent Schroedinger equation (e.g. for spin, calculation may predict it points in any direction in space, but after measurement of spin projection to some specific direction, spin state has to point in one of two opposite directions defined by the measurement setup).

In case of hydrogen atom gas radiating in a tube, nobody's calculating predicted state of a specific individual atom and then checking whether its real state is or is not consistent with that prediction, so the collapse is not involved in this context. The emission spectrum can be approximately calculated by approximately solving the time-dependent Schroedinger equation for a simpler situation - the hydrogen atom in external electric field, without collisions with other atoms - and using Maxwell's equations, or Jefimenko's formulae for fields in terms of charge and current density, to calculate the implied radiation of the atoms.

Ignoring collisions greatly simplifies the model, and the implied spectrum should still show the basic features of the real measured spectra - the sharp emission lines, at roughly the correct positions. Collisions smear the sharp lines into less sharp lines or bands, and may have other effect on the spectrum, which are hard to estimate without analyzing full complex model that takes them into account.

• This is a great answer on its own, but it might be worth noting that you can determine the relative probability for transitions from some initial state using Fermi’s Golden Rule in time dependent perturbation theory. Commented Sep 19, 2023 at 1:50
• @MattHanson Golden rule is a practical rule for estimating transition rates in a non-equilibrium process, this is conceptually not necessarily needed to calculate the emission spectrum. Commented Sep 19, 2023 at 3:17
• Sure, just pointing towards other useful information relevant to the problem. Commented Sep 19, 2023 at 6:02
• Ján, your answer (thanks!) seems to imply that one only knows to apply the notion of wave function collapse after realizing the experiment, which sounds like the theory is then not predictive at all. It's surprising, to say the least. Commented Sep 20, 2023 at 22:12
• @Zatrapilla The theory is predictive even without collapse. It predicts (just based on $\psi$, calculated from the Schr. equation without using collapse) probabilities of positions and momenta of charged particles (and thus of the net electric current density), and thus also expected averages of positions, momenta (and electric current density). Expected average of electric current density can be then used in classical EM theory to predict the spectrum of emission. Commented Sep 20, 2023 at 23:12