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Nov 25, 2021 at 1:15 comment added K. Grammatikos I don't think we disagree so I fail to see what this conversation is leading us to. My point is that at $n$ large the peaks are getting denser. That's all. After all it's the OP that shows a misunderstanding of the concepts and I'm defending QM. Thank you for the reference.
Nov 25, 2021 at 1:14 history edited K. Grammatikos CC BY-SA 4.0
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Nov 24, 2021 at 22:16 comment added Thomas The classical radiation law would not produce any lines. It would make the electron to continuously lose energy and spiral into the nucleus. This is what the OP was referring to, but this is obviously not observed. $n\rightarrow n-1$ lines for $n$ into the hundreds are indeed observed in astronomy. Their line width decreases like $1/n^5$ (see my website plasmaphysics.org.uk/#atdecay (Atomic Decay Probability)), which is faster than the distance between lines decreases ($1/n^3$). Only collisional broadening and the instrumental resolution sets a limit to this.
Nov 24, 2021 at 19:56 comment added K. Grammatikos Yes there will be decays $n\to 1$, sure, but I believe multiphoton decays with small energy denominators should exist and be detectable with a sufficiently low energy resolution. I also have a hard time believing that the $n-th$ energy level is more stable in the presence of an EM field than the ground state. If anything I would assume the opposite. Can you cite your sources or explain why this is the case?
Nov 24, 2021 at 19:49 comment added K. Grammatikos You clearly do not understand what the gist of my answer is. I am not talking about broadening effects coming from many-particle considerations. What I am talking about is a hypothetical situation where you would be able to measure soft photons coming from transitions like $n\to n\pm1$ for large $n$. These peaks are so close together in energy that they effectively would look like a continuum around $E=0$ to a machine with a certain energy resolution. All I'm saying is that the classical radiation law should emerge for VERY low transition energies.
Nov 24, 2021 at 19:36 comment added Thomas What gives you the idea that highly excited atoms would emit continuum radiation? They emit a discrete line spectrum like the lower states as well (see en.wikipedia.org/wiki/Hydrogen_spectral_series ). These lines are merely broadened either by collisions with other atoms or by the finite lifetime of the level as for lower levels As the lifetime of a level increases strongly with n, lines originating from highly excited states tend actually to be sharper than for lower states.
Nov 24, 2021 at 11:47 history edited Ruslan CC BY-SA 4.0
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Nov 23, 2021 at 22:31 history answered K. Grammatikos CC BY-SA 4.0