# Photon and the field generated by an accelerated charge

1. Feb 5, 2010

### DaTario

Hi All

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

2. Feb 7, 2010

### conway

I'm going to try to answer this just so it doesn't slip off the first page.

In general, quantum mechanics doesn't have trouble with electrons radiating because they accelerate classically. I don't know that it especially forbids scenarios like the one described here, supposing you had a tiny charged sphere similar to the "classical" electron. The fact that you don't have such electrons in practise is just a circumstance of the universe. But if there were such classical-style electrons, QM would not especially have a problem calculating the radiation. I don't think its especially different from the calculation for synchrotron radiation (or is it cyclotron?).

In short, if you have a diffration grating in the vicinity of the experiment, and a photographic plate behind the diffraction grating, from time to time a dot would appear on the photographic plate. The position of the dot would correspond to one particular frequency (assuming a big enough grating that you would only get the first peaks for the spectrum of interest). Eventually a density of dots would build up on the plate giving you a visual map of the frequency spectrum.

As far as what that spectrum would be, the QM result in cases like these does not generally differ from the expected classical result.

3. Feb 8, 2010

### Frame Dragger

That makes sense... and you're correct that it's Synchroton.

4. Feb 8, 2010

### PhilDSP

To generally answer a combination of your questions: When an electron in the hydrogen atom makes a transition and either emits or absorbs radiation, the photon will have a wavelength that depends on Bohr radius of the before and after states:

wavelength = $$\frac{4\pi}{\alpha} \left[ \frac{1}{radius_{lesser}} - \frac{1}{radius_{greater}} \right]^{-1}$$

where $$\alpha$$ is the fine structure constant

This is a coarse calculation that doesn't take into account things such as electron spin, for example.

I don't believe anyone has thought to attempt to measure a possible transition time, partly because that is one parameter that cannot be determined according to many interpretations of QM. However, it seems quite reasonable to try to get an upper bound on the time using coherent radiation and then correlating the phase of the in-going radiation against the out-going radiation. There would very likely be a period involved where the electron's revolution would be perturbed before becoming unstable. However that is making a conjecture that probably wouldn't be sanctioned by the typical QM practitioner.

Last edited: Feb 8, 2010
5. Feb 8, 2010

### DaTario

Ok All,

But I think the focus of the question is a little different. I am trying to see if there is some evidence (against or not) of the simillarities between the radiation emitted in a classical falling of an orbiting electron to the proton (nucleus) during some distance (where initial and final points are compatible with two eigenvalues of energy for H atom)and the photon itself emitted in this same situation (i.e. transition).

To PhilDSP, does this equation has some relation to the radiation emited by a classically electron like charge orbiting a classically proton like charge between these two positions (radius)?

Best Regards,

DaTario

6. Feb 8, 2010

### PhilDSP

Yes, it's exactly that for the hydrogen atom according to Bohr's formulation. It works for both emitted radiation and absorbed radiation.

7. Feb 8, 2010

### SpectraCat

Have you seen this paper?

http://www.calphysics.org/articles/ColeHydrogenPRE.pdf" [Broken]

Last edited by a moderator: May 4, 2017
8. Feb 8, 2010

### PhilDSP

That's quite nice, thanks!

Last edited by a moderator: May 4, 2017