# Field of an accelerated electron falling down to nucleus versus photon

1. Aug 10, 2005

### DaTario

Assuming the electron is orbiting (semiclassical approach) the nucleus at the second allowed distance from it (2s, for example in H). When the electron decays (classical electrodynamics) it probably will do it in a kind of spiral trajectory. This trajectory implies acceleration and so, a radiation will be sent due to this decay. How does it relates to the concept of photon ?

Note: when the electron find the first (fundamental) orbiting radius we (ad hoc) stop it from falling down.

Best Regards

DaTario

P.S. I guess that from this classical problem one could find out the coherence lenght of this radiation train, the spectrum of it and may be something more, so that comparison with experimental results seems to be possible.

references will be appreciated

Last edited: Aug 10, 2005
2. Aug 10, 2005

### tdunc

Here,

And Electron is a
http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator

That is in a
http://en.wikipedia.org/wiki/Atomic_Orbital

or
http://en.wikipedia.org/wiki/Energy_state

That changes by way of a
http://en.wikipedia.org/wiki/Quantum_leap

And releases a
http://en.wikipedia.org/wiki/Photon

http://en.wikipedia.org/wiki/Ground_state

"field of an accelerated electron falling down to nucleus versus photon"

The electron itself in motion could be considered a field, um.. somebody else take over.

3. Aug 10, 2005

### marlon

:rofl: ok, here is your FIRST mistake : this does not happen according to QM !!!

marlon

ps have you read the 'socalled easy pieces' entry in the elementary particles presented thread ? Guess not...you know what to do now...

4. Aug 10, 2005

### DaTario

Ok, I know QM does not allow this statement. This was the reason I wrote "semiclassical approach" which means we are assuming the electron has trajectory be we deal with the quantum feature of discretized energy levels (Bohr radius and all that).

Trying to restate the question.

Assuming the electron in a Hydrogen atom has a well defined orbit around the nucleus, but its energy levels are quantized, we may work out the radiative transition from the second quantum mechanically allowed orbit to its fundamental state. From this classical electrodynamics problem we are likely to obtain the full characterization of the radiation emited by this system (electron + nucleus) while the electron is falling in a spiral to the fundamental state. This full characterization involves spectrum, polarization features, energy, etc. How does this classically calculated radiation relates to the photon (full QM way) emited by the corresponding transition ?

Best Regards and thank you for reminding my mistakes.

DaTario

5. Aug 10, 2005

### DrChinese

This question does not make sense because this area is where the classical picture falls apart. The classical atomic model never agreed with experiment, which was the problem all along.

The logical question is: "How does the QM model relate to experiment?" It agrees very well, but somehow I think you are aware of that already.

6. Aug 10, 2005

### marlon

The electron has NO well defined orbit around the nucleus. Do you not know what an orbital is ?

Do you realize that the circular orbit model has indeed it's place in history BUT it is not correct ? This is only important because of the concept of quantization and it needs to be looked at as a preliminary atomic model, that is all. I mean, you don't see me asking questions about the Plum Pudding model right ?

marlon

7. Aug 10, 2005

### DaTario

I perfectly agree with you on what you said, but there is some regimes in which assuming the electron has an orbit around the nucleus makes sense (Rydberg atoms for instance). My question is about the shape of the radiation that would come out from the electron + nucleus if the electrons fell down spirally due to the charge acceleration's loss of energy. In what aspect does this classical result depart from experimental evidences about photon features ?

I am just looking for a classical model for the photon.

The electron spiralizes -> accelerates -> emits radiation. And this radiation I would like to know, and to verify if it is completely different from what we get with our experiments with "the photon".

Best Regards

DaTario

8. Aug 10, 2005

### marlon

No that is not true.
What on earth is that ?

??? Shape of radiation ? What is that ?

Again, read the 'socalled easy pieces'-entry , please, otherwise, accidents WILL happen.

YOU NEED TO KNOW THE TRUTH, and yes i assure you : YOU CAN HANDLE THE TRUTH

you are on your way to heaven

marlon

9. Aug 10, 2005

### DaTario

Thank you for sharing part of your wisdom with me. For Rydberg atoms

Quantum Optics
- Including Noise Reduction, Trapped Ions, Quantum Trajectories and Decoherence
M. Orzag
Springer 1999

10. Aug 10, 2005

### marlon

Well this is a bit contradictory, since the very foundation of quantum optics will contradict with your orbit model.

Another thing, i asked you what Rydberg atoms were. Please, do not answer me with links i cannot verify/consult directly. Just explain to me what they are, since you must know this.

marlon

11. Aug 10, 2005

### DaTario

I am referring to acceptable aproximative procedures, and not to rigorous concept manipulation.

But anyway, either you study this subject and start bringing something which is related to my topic or I will stop answering your small provocations.

12. Aug 10, 2005

### DaTario

I supose you have authority. If you claim you have authority you should support it with your own efforts.

13. Aug 10, 2005

### marlon

If i insulted you, i apologize.

Well as an "authority" i do not know this concept you are talking about. So, please, i ask you what this Rydberg atom is ? How does it differ from a 'QM atom' described in terms of orbitals. Is this Rydberg atom compatible with the QM-theory ? Can it also be described with orbitals ? If so, what adaptation does one need to make in order to go from 'just an atom' to a Rydberg atom ?

Is there any experimental backup for its existence ? If so, you can give me some links to journals like Phys Rev or Nature or...

I am not being sarcastic here, just curious and eager to learn something new. That is all.

regards
marlon

ps : and what is 'an acceptable approximative model' How is it defined and when do you know it is acceptable? does this apply to the Rudberg atom ? If so, can you tell me how ? I mean, how do i go from QM to the approximative model and in what physical regime is it valid ?

are you referring to this ?

Last edited: Aug 10, 2005
14. Aug 10, 2005

### Hans de Vries

A classical electron in the Bohr orbit would emit radiation at circa 45.5 nm.
Twice the frequency of that belonging to the orbit (13.6 eV). This factor two
is also found for the higher orbits which have their maxima at n2 the bohr orbit.

You see what kind of frequencies you would get in a classical down-spiraling
picture. So it's is very different from the QM picture where the frequency
stems from the difference of two energy levels.

Regards, Hans

Last edited: Aug 10, 2005
15. Aug 10, 2005

### Hans de Vries

Classical EM field theory is not neccesarily in conflict with the non-radiating
QM orbits.

That is, if you take the electric charge to be evenly divided (smeared out)
over the entire wave function. Acceleration can be defined with the help
of the density and momentum operators. Now for each acceleration there
exist an exactly opposite acceleration at the opposite side of the wave-
function and the average acceleration becomes zero.

Molecular Modeling software assumes charges to be smeared out in this
way because it gives the results closest to experiment.

Using opposite charge accelerations to suppress radiation is a technique as
old as the twisted pair wires of your phone subscriber line and is used
extensively today in those multi GHz busses in the modern PC's

Regards, Hans.

Last edited: Aug 10, 2005
16. Aug 11, 2005

### DaTario

Hi Hans,

Would you have some reference to give me, concerning the classical estimative of frequencies and its departure from quantum (and experimental I presume) results for the problem I alluded ?

Marlon

Sorry.
Rydberg atoms are Hydrogen like atoms whose electrons are in highly excited states (typically n = 50). In such situations, the classical model for the atom (planetary) still presents departures from experimental and quantum description, but they are smaller. So that, to some extent, one can use the classical picture to get some physical results or some intuitive reasonings, without getting too far from what really happens (?) and from QM says.

Quantum optics books in general deals with it.
Perhaps the following references will help.

PRA 44, 7804 (1991)
PRL 58, 353 (1987)
PRA 48, 803 (1993)
PRA 36, 740 (1987)

I believe there must be more specialized literature on this subject. I sent you references of papers on micromaser, which is one of the main applications of Rydberg atoms I am aware of.

Sorry for not treating you as I should, i.e., gently. I am happy of having found a place where people discuss physics. I must congratulate you for the good job. I also recognize that reading fuzzy statements is something terrible. I try to put ideas in words with precision, but I know I have some steps to get there.
Thank you anyway.

Best Wishes

DaTario

17. Aug 11, 2005

### Staff: Mentor

A "Rydberg atom" is (using hydrogen to be specific) an atom in a just-barely-bound state with a very large value of the principal quantum number $n$.

I have read that in a Rydberg atom you can have the electron behaving very much (although surely not completely!) as if in a semiclassical "planetary" model. However, I would expect that in order to have the electron behave as a localized planet-like object, its wave function would actually have to be a superposition of several closely-spaced energy states.

I don't have any specific references handy, but I once had a colleague here who collaborated on experiments involving Rydberg atoms at the University of Kentucky. A Google search on "rydberg atoms kentucky" led me to this page.

18. Aug 11, 2005

### marlon

thanks jtbell, for the info

marlon

19. Aug 11, 2005

### Blackforest

I find this item a perfect illustration of the permanent difficulties arising from any try to find a convenient picture between a classical representation and a quantum one. As Dc Chinese said:"The classical atomic model never agreed with experiment, which was the problem all along." I find this context (electron surrounding a proton) a fascinating one to test my own reseach too. It is well-known that gravitation's effect are extremly week if compared to the EM one; I suppose that it is also true inside a H atom. Does these circumstances allow an analyse of the distant source (proton) on the electron as it is for example made in Missner Thorne and Wheeler (Gravitation; chapter 19; 1973)? That is: "Can we suppose that the geometry around an electron is asymtotically flat and try to scrutenize the imprints of the angular momentum of the proton on the surrounding electron as we are actually doing it around the earth with the satellite Gravity Probe B? Does this kind of representation makes sense within an atom?

As you understand: it is my essay to built a bridge between a "classical" or relativistic representation and the quantum representation.

Perhaps one more time an impossible challenge... Don't matter. Thanks in advance for discussion.

20. Aug 11, 2005

### Hans de Vries

You can simply assign a speed to a classical electron at a certain radius by
taking its angular momentum as a multiple of $\hbar$. That's what I did in the
example. Speeds would then be in the order of c/137.

More specifically what you want might be found here:

D. C. Cole and Y. Zou
"Analysis of orbital decay time for the classical hydrogen atom interacting
PHYSICAL REVIEW E 69, 016601 (2004)
http://www.calphysics.org/articles/ColeHydrogenPRE.pdf

As I said, there's no chance to get a point particle to generate anything
like the QM orbitals. The first thing which would be necessary in such an
attempt is to have the charge smeared out evenly over the entire wave
function to stop it from radiating energy away.

This doesn't mean that people stop trying though, but they use extra
presumptions like "Zeropoint Radiation" See for instance:

D. C. Cole and Y. Zou, “Quantum mechanical ground state of Hydrogen
obtained from classical electrodynamics,” Phys. Lett. A 317, 14-20 (2003).

http://www.calphysics.org/articles/ColeHydrogen.pdf

They do get a thing which looks a bit like the ground state, which is
interesting but still very far away from predicting the basic Lyman,
Balmer and Paschen series, let alone all the finer and finer details which
are predicted by the Schroedinger Equation, the Dirac equation and finally
QED with it's very high precision predictions.

Regards, Hans.