Radiative Equilibrium Without Quanta: Normality

Consider a Hydrogen atom described by Schrödinger's Equation SE in radiative equilibrium with light of a certain frequency $\nu$ described by Maxwell's equations as an  electromagnetic wave. This means that there is a gap $\Delta E$ in the distribution of eigenvalues $E$ or spectrum such that $\Delta E =h\nu$ with $h$ a scaling factor, in classical literature named Plank's constant. 

The SE for Hydrogen is a partial differential equation of classical continuum form in terms of a wave function which changes continuously in space and time during the process of establishing and maintaining radiation at the resonance frequency $\nu$. The energy gap $\Delta E$ scales with the frequency $\nu$ over  the spectrum. 

What is discrete is the spectrum, just as in classical continuum mechanics, while wave functions are continuous and do not take any discrete "jumps" in state/energy.  

Conclusion: The Schrödinger's Equation SE for a Hydrogen atom takes the form of classical continuum mechanics. QM for a Hydrogen atom is classical continuum physics. No need for quantisation. The fact that the spectrum is discrete is not evidence that any non-classical process of quantisation is really needed. See also this post.

chatGPT: Maxwell + Schrödinger looks good:

• Treat the atom quantum mechanically (Schrödinger equation).

• Treat the radiation as a classical wave (Maxwell).

• That explains a lot: absorption spectra, stimulated emission, radiative equilibrium, Rabi oscillations.

• Everything looks continuous.

This model works surprisingly well in many normal conditions.

end chatGPT

But a modern theoretical physicist is not happy with normality of classical continuum physics as description of the basic problem of atom physics of a radiating atom, because it is not modern new physics. And so the modern physicist goes on to confront the radiating atom as classical continuum physics with some extreme circumstances such as very very weak forcing so weak that the continuity breaks down. Like running your car engine with only a very weak slow irregular ignition making the engine start to malfunction. This is called appeal to extremes often used in debate.

By focussing on some extreme case, the classical model covering the normal case can be downplayed as "wrong" even if it works fine, to prepare the way for some new bold modern theory, which is more "fundamentally correct". In this way all the victories of the classic theory for all normal cases can be cashed in for the new theory to which can then be added anything extreme even if vague. 

This is what is done when General Relativity replaces Newton's theory of gravitation as being more "fundamentally correct". Or when QFT replaces QM which replaces Schrödinger+Maxwell. More and more extreme to downplay the normal.

So can unsuccessful explanation of something normal within classical continuum mechanics, be covered up by focussing the interest onto something more fundamental and extreme, and the possibility of a classical explanation can be missed, as that of RealQM.