# Classical interpretation of the photoelectric effect

1. Oct 7, 2013

### MalachiK

I've been reading through the posts on this forum that deal with the photoelectric effect as evidence for the quantization of the EM field. In all of the introductory texts I've read, the cut off frequency and the dependence of the photoelectron energy on the frequency of the light are presented as proof that light is absorbed by the material in discrete packets.

For example, in the MIT online lecture notes for a course on elementary QM we find a statement about the historical development of the quantum theory that says that Einstein was able to explain the photoelectric effect by assuming the reality of the 'quanta' that Planck had used to come up with the solution to the ultraviolet catastrophe. The hyperphysics site says pretty much the same thing.

On the other hand, I occasionally read claims that the photoelectric effect in fact only demonstrates the quantum behavior of the electrons and that a classical treatment of the EM field is sufficient to yield the observed experimental details. While I'm in no mood to wade into the maths myself on this one, maybe there's someone on this forum who's already thought this through? I have a hard time believing that all of the introductory texts are both historically and physically incorrect. On the other hand, I've got this paper from 1968 that I keep meaning to work though that seems pretty legit. (The problem with being mathematically lazy is that you find yourself having to evaluate competing arguments from authority all of the damn time!)

I suspect the answer is that the classical treatment kind of works in limited cases but the quantized field is needed to make sense generally. Is this correct?

2. Oct 7, 2013

3. Oct 7, 2013

### dextercioby

A theoretical model in which matter is treated quantum mechanically and is interacting with a classically described e-m radiation field is called 'semiclassical'. The article by Lamb is the semiclassical treatment of the photoelectric effect.

4. Oct 7, 2013

### MalachiK

So since it's possible to construct a semiclassical explanation it seems that quantized light isn't required to explain the photoelectric effect. Is it taught this was purely for pedagogical convenience, or is there some experimental details that the semiclassical approach doesn't account for?

5. Oct 7, 2013

### jarekd

It again takes us to discussion what is quantum and what is not ... generally the fact that there are waves conjugated with the corpuscle is one of features quantum mechanics extends the classical one and it is required for Bohr-Sommerfeld quantization condition for electrons, what is required for that their energy differences (emitted as photons) are also quantized.
So I would say that photoelectric effect is a quantum one, but sure it can also be seen from classical field theory perspective - exactly like for Couder's walking droplets. Pure classical mechanics is not enough as it doesn't propagate waves in the medium.

6. Oct 7, 2013

### bhobba

Einstein explained the photoelectric effect without the full machinery of QM - because it wasn't even around then. So obviously it can be done. But you need QM to explain that and a myriad of other experimental results taken together. QM is the only theory known that does all that - and more besides.

Thanks
Bill

7. Oct 7, 2013

### atyy

Alain Aspect comments on the issue that field quantization is not needed to explain the photoelectric effect - see around 28:00 of his talk. Aspect explicitly mentions the Lamb and Scully model mentioned in the OP. The photoelectric effect requires quantization of matter or light, and one can explain it with quantization of matter without quantization of light.

What then requires field quantization? The Lamb shift is usually considered to be an effect that requires field quantization.

Last edited by a moderator: Sep 25, 2014
8. Oct 8, 2013

### Jano L.

It is a sad situation, but even the best intro textbooks do have such considerable defects. It takes quite a time to include the continual development of the science into textbooks, especially if it concerns some deeply rooted misconceptions. One book that is better in this respect is Ballentine's Quantum Mechanics: A modern perspective.

The reason most books show photoeffect as a proof of quanta is because of the success of the Einstein photoelectric equation for the stopping potential $U$ required to stop electrons ejected by the light of frequency $\nu$

$$h\nu = A + qU,$$

which Einstein based on the idea of light quanta with energy $h\nu$.

Before the discovery of Schroedinger's equation in 1925, the equation was a miracle and seemed as direct proof of light quanta.

However, after Schroedinger's papers and further development, people slowly began to realize that the above equation is not that mysterious and perhaps can be explained as a kind of resonance response of the atoms to the oscillating EM wave. That is essentially what Schroedinger's equation leads to.

It is also very instructive to look on the dependence of the photoelectric current on the frequency of light. The curve is continuous and exhibits several continuous peaks, not discontinuous jumps which would be most natural for the quantum concept.

Very good book on this important question is

Concepts of Quantum Optics by P. L. Knight and L. Allen (Oct 1983)

It contains reprints of the original papers on this. Also great is the Jaynes paper
`Survey of the Present Status of Neoclassical Radiation Theory
http://bayes.wustl.edu/etj/articles/survey.nct.pdf

Later the center of discussion shifted to phenomenons where relativity plays larger role. As atyy says

Lamb shift can be qualitatively explained (Jaynes) without field quantization, via coupling to harmonic bath, or even internal interactions (referred often to as self-interactions) lead to frequency shifts:

http://bayes.wustl.edu/etj/articles/electrodynamics.today.pdf

What seems to be the main argument for quantization these days are the coincidence detector counting experiments of Grangier, Roger and Alain Aspect, like

P. Grangier, G. Roger and A. Aspect, Europhys. Lett. 1, 173 (1986).

and later similar experiments under "quantum optics". The relevance of these experiments for the pro-photon efforts have been challenged by some physicists who propose alternative explanations based on SED:

http://arxiv.org/abs/quant-ph/9711046
http://crisisinphysics.wordpress.com/category/quantum-crisis/

9. Oct 8, 2013

### MalachiK

That's great. Just what I was after! Thanks very much guys.

10. Oct 9, 2013

### kof9595995

11. Oct 9, 2013

### ZapperZ

Staff Emeritus
12. Oct 9, 2013

### MalachiK

Thanks, Zapper. I must have missed that one when I was searching though the site before I posted.

One of the points you raised in the thread you linked to is something that occurred to me when I was thinking about this the other day. In the semiclassical treatment in the Lamb paper and in the video posted above, there seems to be this idea that the electron is excited out of some sort of quantized state in the metal. My understanding of solid state physics from my distant undergraduate days is that the de-localized electrons in the metal exist in a continuum of states (although I also recall working with some sort of periodic potential due to the lattice, so err... yeah.)

I kind of get the idea that the interaction between the classical wave and the quantum atom can be thought of as some sort of resonance energy transfer to the electron, but surely this requires the electron to be rolling about in some sort of potential well (or existing as a superposition of various stationary states in the QM model). I've always imagined the electrons in the metal as existing as a gas with a continuous range of energy values.

Once again, I feel I'm approaching this from the wrong end and I should probably go away and learn the quantum theory properly from the beginning.

13. Oct 9, 2013

### ZapperZ

Staff Emeritus
Your memory is correct. The typical photoelectric effect is primarily due to the conduction electrons, and these electrons are in an energy band. You don't see or detect any discrete energy levels here. So it is difficult to see any form of "quantization" from the material's end of this.

As I've stated in the previous thread that I linked to, the photoelectric effect is actually a rather naive and simplistic phenomenon. While that can probably be described with semi-classical model, this model has failed or haven't been used to attempt to describe more complicated photoemission phenomena of various types, such as the multiphoton photoemission that I've mentioned. We have progressed significantly since Millikan's experimental test of the Einstein's model!

Zz.