# I Can electrons transition collectively, emitting 1 photon?

1. Oct 28, 2016

### 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.

2. Oct 28, 2016

### 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.

3. Oct 28, 2016

### TubbaBlubba

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.

4. Oct 28, 2016

### 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.

5. Oct 28, 2016

### TubbaBlubba

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

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

6. Oct 28, 2016

### houlahound

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

7. Oct 28, 2016

### TubbaBlubba

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.

8. Oct 28, 2016

### 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.

9. Oct 29, 2016

### bhobba

10. Oct 29, 2016

### TubbaBlubba

11. Oct 29, 2016

### 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.

12. Oct 29, 2016

### TubbaBlubba

Excellent point. Thank you.

13. Nov 1, 2016

### f95toli

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.

14. Nov 1, 2016

### houlahound

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