I Can electrons transition collectively, emitting 1 photon?

[TubbaBlubba]

Basically, I'm asking about loosely-bound electrons, e.g. everyday static electricity. Can their combined wavefunction evolve to a low-energy state "at once", so that they emit a single high-frequency photon, rather than multiple photons of energies suggested by the potential difference?

If not, what is the deeper theoretical reason for it? How does it differ from the collective excitation of a nucleus?

As a 3rd (final) year undergrad this question hasn't occurred to me. I've taken introductory courses in QM, Subatomic, Statistical and Atomic-Molecular physics (exam on Monday actually). I have not taken courses in Solid State Physics (that's next term) nor in Lagrangian/Hamiltonian mechanics (that's my next course).

Thanks.

 

[houlahound]

Free electron laser perhaps?

How do moles worth of electrons all combine coherently as you seem to suggest. Only thing close I can think of are Bose Einstein condensates and phonons...not electrons.

By definition static electricity is incoherent.

 

[TubbaBlubba]

Free electron laser perhaps?

How do moles worth of electrons all combine coherently as you seem to suggest. Only thing close I can think of are Bose Einstein condensates and phonons...not electrons.

By definition static electricity is incoherent.

I'm not sure. I was thinking of collective movement across a potential from one bound state to another resulting in a greater photon frequency than the potential difference suggests.

 

[houlahound]

The collective movement seems a problem with thermal electrons with random phases.

Secondly as basic QM showed the frequency is only dependent on the energy difference and independent of how many objects making the transition.

 

[TubbaBlubba]

The collective movement seems a problem with thermal electrons with random phases.

I'm imagining it as a rare but theoretically possible fluctuation.

Secondly as basic QM showed the frequency is only dependent on the energy difference and independent of how many objects making the transition.

Sure, but I have only studied many-electron systems and combined wavefunction shallowly. Pretty far removed from "particle in a box".

 

[houlahound]

Think photoelectric effect, more photons below the threshold frequency will not eject an electron no matter how intense the beam.

 

[TubbaBlubba]

Think photoelectric effect, more photons below the threshold frequency will not eject an electron no matter how intense the beam.

I thought of that as an inverse analogy, yeah, but that would involve multiple photons and a single electron. The symmetrical inverse would be multiple electrons simultaneoysly absorbing a high-energy photon without being ejected. Presumably one could attempt to painstakingly observe it using a single-photon source.

 

[Khashishi]

As long as the selection rules are obeyed, it should be possible. The initial and final electron states should have angular momentum that differs by 1 unit, and if the initial and final states are symmetric, they can't have the same parity.

 

[bhobba]

Yes - but with very very low probability. Other processes are of much much higher probability.

Its tied up with the fact the electron is coupled to the quantum EM field that permeates the universe. Its one of the first indications we need QFT:
http://www.physics.usu.edu/torre/3700_Spring_2015/What_is_a_photon.pdf

Thanks
Bill

 

[TubbaBlubba]

Yes - but with very very low probability. Other processes are of much much higher probability.

Its tied up with the fact the electron is coupled to the quantum EM field that permeates the universe. Its one of the first indications we need QFT:
http://www.physics.usu.edu/torre/3700_Spring_2015/What_is_a_photon.pdf

Thanks
Bill

Thank you!

 

[A. Neumaier]

Since all electrons are indistinguishable, and there is no precise notion of ''outer electron'' (except in the Hartree-Fock approximation), any transition must be regarded as being a collective behavior of the electron field as a whole.

 

[TubbaBlubba]

Since all electrons are indistinguishable, and there is no precise notion of ''outer electron'' (except in the Hartree-Fock approximation), any transition must be regarded as being a collective behavior of the electron field as a whole.

Excellent point. Thank you.

 

[f95toli]

The answer is indeed yes.
There is a whole sub-field of experimental QM where people study large ensembles of spin interacting with for a example a microwave cavity, i.e. it is basically the generalization of "standard" cavity-QED (single spin 1/2 in a cavity) to a situation with many spin 1/2 systems. See Tavis-Cummings Hamiltonian.

There are papers out there showing store and retrieval of single photons using relatively large (10^10 or so) spin systems.

 

[houlahound]

And how is there frequency different to the single spin emission frequency?