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Suppose an electron is orbiting (in classical sense) a proton at a given distance (compatible with, i.e., less than the experimentally determined value for atomic radius of Hydrogen). Let's call this initial distance R3. From classical view point this orbit has a well defined frequency (F3) and a well defined energy (E3). Also from classical arguments follows that this orbit will decrease its radius in time due to loss from accelerated charge emissions of radiation. So after a given time T this electron will reach another radius R2< R3. I know that, at this new distance R2, the frequency of the orbit has another value (say, F2) and the energy has changed to, say, E2.

Now suppose that R3 is the mean radius of some quantum state with E = E3 and R2 corresponds to the quantum mean value of radius for a given state with E = E2.

My questions are:

1) Classically, the EM pattern of emission of radiation referred above can be completelly described. So, how does this EM pattern relates with quantum photon generated in the transition from state 1 (with E = E3) to state 2 (with E = E2) ?

2) How F3 and F2 relates with the frequency f = (E3 - E2)/h of the experimentally detected photon from the referred transition ?

3) How does the classical time T of transition relates to the coherence time of the experimentally detected photon of this same transition ?

4) Which are the pitfalls in this discussion ?

5) references ?

Thank you

DaTario

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# Possible similarity between Classical and Quantum photon definition

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