frequency of EM wave in classical and quantum physics

[donniedarko]

in classical physics, when a charged particle oscillates, it emits an electromagnetic wave, and the frequency of the wave depends on the frequency with which the particle oscillates.
But in quantum physics, when an excited atom emits a photon, the energy of the photon depends on the magnitude of the quantum leaps that the emitting electron makes (if it jumps one level, the photon will have a certain energy; if it jumps two, a greater energy, and so on). So the frequency of the electromagnetic wave that corresponds to the photon will depend on the amplitude of the quantum leaps made by the electron.
I don't understand why these two cases are so different. In analogy with the classical case, shouldn't the frequency of the wave emitted by the atom depend on the frequency with which the electron makes quantum jumps? Or is there a quantum explanation of the classical case that I don't understand? I know that classical physics cannot be used to explain quantum phenomena, but it seems strange to me that there is this asymmetry in the two cases. Sorry in advance if the question is dumb; I am approaching quantum physics because it is a topic that I am very passionate about, but I have a totally different background ... thanks if you can clarify me in a simple way!

[exchemist]

40 minutes ago, donniedarko said:

in classical physics, when a charged particle oscillates, it emits an electromagnetic wave, and the frequency of the wave depends on the frequency with which the particle oscillates.
But in quantum physics, when an excited atom emits a photon, the energy of the photon depends on the magnitude of the quantum leaps that the emitting electron makes (if it jumps one level, the photon will have a certain energy; if it jumps two, a greater energy, and so on). So the frequency of the electromagnetic wave that corresponds to the photon will depend on the amplitude of the quantum leaps made by the electron.
I don't understand why these two cases are so different. In analogy with the classical case, shouldn't the frequency of the wave emitted by the atom depend on the frequency with which the electron makes quantum jumps? Or is there a quantum explanation of the classical case that I don't understand? I know that classical physics cannot be used to explain quantum phenomena, but it seems strange to me that there is this asymmetry in the two cases. Sorry in advance if the question is dumb; I am approaching quantum physics because it is a topic that I am very passionate about, but I have a totally different background ... thanks if you can clarify me in a simple way!

The two cases are not quite as different as you may think. In QM the emission of a photon is driven by something called a "transition dipole moment": https://en.wikipedia.org/wiki/Transition_dipole_moment. You can think of this as somewhat analogous to the oscillating dipole created by an oscillating electric charge.

A transition dipole moment can arise due to an electron moving between orbitals in an atom or molecule, or it can be something more obviously "physical", like the change in vibration state of a molecule with a dipole moment (molecules with no dipole moment do not emit or absorb in the infra red) or a change in the rotational state of a molecule (again, molecules with no dipole moment do not emit or absorb microwaves).

So you still need some kind of oscillating or rotating dipole moment in order to emit or absorb EM radiation, even when modelling it by QM.

The fact that the frequency of the radiation is determined by the energy difference between the two states is however not something the classical picture can account for. This goes right back to what Einstein got his Nobel prize for (the photo-electric effect and Planck's E=hν).     

Edited January 21, 2022 by exchemist