The Photoelectric Effect question

[ZapperZ]

You are still avoiding answering my question. Show me how, by putting together classical E&M and the Schrodinger equation, you get explain the Photoelectric effect using the wave equation. I've checked your earlier posts, and you've shown nothing. The Photoelectric effect is MORE than just describing what happens at the threshold. You also have produce no QUANTITATIVE description for one to double-check against the experiment.

It is obvious that you are not using any of the already published references available in the literature. This tells me that this is your own personal pet theory with no valid, published references. Maybe you'd like to read the PF Rules first before you proceed any further.

This is the last time I will ask you to show such derivation.

Zz.

 

[Peter Morgan]

I don't know what all those models are but it doesn't sound like what I meant. I thought you could explain the photo-electric with a basic description where the electron is given by the Schroedinger wave function and light is given by Maxwell's equations. At least to the extent which Einstein described it in 1905. That's what I meant when I said I hadn't put anything forward that was "out of whack" with standard QM. Would you say I'm wrong in holding this opinion? And if so, where does my model fail to explain the points covered by Einstein's theory?f (I'm not asking about ZapperZ's multi-photon cases here, I'm just asking about the basics that Einstein attempted to explain in 1905.)

Hi Marty,
I think you've chosen the wrong territory, quantum optics, to have a battle. This is an area in which there is a huge amount of experiment and technology that can be adequately described to good accuracy by QM. There are lots of experiments that can be modeled semi-classically, but not all have been successfully so modeled. Semi-classical modeling is sufficiently well-developed that, knowing where it can be used, Physicists sometimes use these methods (I wouldn't be surprised if ZapperZ et al. do sometimes use these methods, even that they teach them; but I also wouldn't be surprised if they don't), but I think there is a sense in which semi-classical modeling is not a clean a way to think (sorry that's so woolly).
If you managed explicitly to model every experiment that is well-described by quantum optics using semi-classical methods, you would probably end up with a model that looks like Stochastic Electrodynamics, which is one way to accommodate a great deal of the experimental evidence. Even if your system for creating models did not look much like SED, it's unlikely, unless you are a good mathematician, that your system would look as pretty and be as good for engineering as the quantum optics formalism. Physicists and engineers also care about how easy it is to think about experiments within a formalism, and to create empirically effective models.
The complexities of SED or something like it are what you get when people who are as enthusiastic as you have been here to replace QM with something they feel they understand more attempt to engage with all the experimental evidence. The originators and developers of these models worked very hard to construct a mathematically beautiful theory, but although their approaches certainly have merits, they have been judged by Physicists (including me, for what it is worth, and insofar as I am a Physicist) ultimately to have failed.
Physicists are not defensive at all on this territory. They have huge confidence that QM works and works well. They will keep up the put up or shut up argument for a long time.

Better to pick a territory where they are less at ease (this is a terrible metaphor, but this sequence of posts has seemed so combative as to almost require it). The territory I choose is renormalization (although there is a worrying trend of Physicists claiming that the renormalization group is beautiful mathematics). Feel welcome to join me on my topic, https://www.physicsforums.com/showthread.php?t=204567", where I have begun a skirmish on this front. Although the mathematical and conceptual tools I use may not be to your taste, and may in the end not prove to be empirically adequate, something at least as mathematically and conceptually beautiful and powerful as I use there is necessary. IMO, again for what it is worth, is that semi-classical methods won't do.
Of course endless protagonists have pointed at one thing or another in QM and said that that one thing is QM's weak point, so I will probably join them in the dust in due course.

 

[monish]

Show me how, by putting together classical E&M and the Schrodinger equation, you get explain the Photoelectric effect using the wave equation.The Photoelectric effect is MORE than just describing what happens at the threshold.

Are you agreeing that I've correctly described what happens at the threshold?

You are still avoiding answering my question...I've checked your earlier posts, and you've shown nothing.

Well, the threshold frequency was supposed to be the big thing that the wave theory couldn't explain. So that's why I started there.

You also have produce no QUANTITATIVE description for one to double-check against the experiment.

I thought it was clear from my description that by taking the difference in energy levels between the lowest free state and the highest conduction band, you'd get the actual threshold frequency.

I agree with you that there is more to the photo-electric effect than what goes on at the threshold frequency. It's just that this is the only point that has been raised so far in opposition to the wave explanation. If you would like to raise any other points, I would be glad to try to deal with them.

It is obvious that you are not using any of the already published references available in the literature. This tells me that this is your own personal pet theory with no valid, published references. Maybe you'd like to read the PF Rules first before you proceed any further.

This is the last time I will ask you to show such derivation.

Zz.

Fair enough. Which rule am I breaking?

 

[ZapperZ]

Are you agreeing that I've correctly described what happens at the threshold?



Well, the threshold frequency was supposed to be the big thing that the wave theory couldn't explain. So that's why I started there.



I thought it was clear from my description that by taking the difference in energy levels between the lowest free state and the highest conduction band, you'd get the actual threshold frequency.

This is it?

This is well-known even BEFORE QM came in. You do not need to have QM at all to be able to obtain the work function, which is essentially what you are doing. Yet, all the brains in the world at that time couldn't use classical E&M to solve this. Show me how you apply the wave theory to actually produce a result consistent with the Photoelectric effect experiment. None of the semi-classical scenarios that claim to make such a comparison are anything like what you are claiming.

BTW, I'd like to see how you actually use "quantum mechanics" to get the different work functions for the various metals. How were you able to calculate the bandwidth of the conduction band below the vacuum level?

I agree with you that there is more to the photo-electric effect than what goes on at the threshold frequency. It's just that this is the only point that has been raised so far in opposition to the wave explanation. If you would like to raise any other points, I would be glad to try to deal with them.

Read Millikan's paper that verified the Einstein's photoelectric effect model. Did you think he only verified just ONE aspect of it?

Fair enough. Which rule am I breaking?

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Zz.

 

[monish]

This is it?

This is well-known even BEFORE QM came in. You do not need to have QM at all to be able to obtain the work function, which is essentially what you are doing.
Zz.

How do you get the work function without quantum mechanics?

 

[ZapperZ]

How do you get the work function without quantum mechanics?

I know how to get the work function. The question is, DO YOU? You seem to think this is a trivial exercise. It isn't. It requires a band structure calculation that is tied to how the crystal lattice is formed and the valence shell of the atoms making up the solid. It isn't trivial!

So show me how. Please do this in your next post, because this will be the last time I will entertain you avoiding a direct answer to my question.

Zz.

 

[cesiumfrog]

I know how to get the work function. The question is, DO YOU? [..] Please do this in your next post, because this will be the last time I will entertain you avoiding a direct answer to my question.

Mentor, is your purpose to demonstrate your personal superiority? You have said it is possible to obtain the work function without using QM. I'm more interested in learning how that is done, than what I am entertained by watching who can perform on cue the exercises set by the mentor.

When I briefly perused Einstein's paper, I thought he only modeled one aspect of the photoelectric effect (light frequency dependence of ejected electrons), but I'll check which aspects Millikan tested. Since you're already familiar with Mandl & Wolf's "standard semi-classical" approach (whereas, judging from post 10, Marty's "independent" approach is inspired by only your brief description), could you tell me 1) whether that approach can be correctly characterised as treating the electron according to Schroedinger's eq. and the light as a classical wave, and 2) which tests does the "standard semi-classical" model fail?

My personal idea here is that, if the answers are 1) yes and 2) none, than it cannot really be correct to argue that the PE implies anything about the nature of light. If (2) has a different answer, I hope to use aspect (2) of the PE as a simple (and honest) example (possibly preferable to Compton scattering and Feynman's observation that photodetectors click discretely) for teaching the existence of photons.

 

[ZapperZ]

Mentor, is your purpose to demonstrate your personal superiority? You have said it is possible to obtain the work function without using QM. I'm more interested in learning how that is done, than what I am entertained by watching who can perform on cue the exercises set by the mentor.

You've already misread the posts in here once. You might want to pay a closer attention before you make another accusation.

One can already get the idea of the existence of the work function without knowing any "theoretical" description. This is known before QM because one had a phenomenological description of the photoelectric effect. If you don't believe it, try it in an intro physics class. Give them the apparatus, and without teaching them the photoelectric effect, ask them to do the set of necessary experiments. They'll find for themselves the threshold value without having to invoke knowledge of QM. In fact, there are schools now that are teaching physics this way, via self-discovery before they are introduced to the theory.

When I briefly perused Einstein's paper, I thought he only modeled one aspect of the photoelectric effect (light frequency dependence of ejected electrons), but I'll check which aspects Millikan tested. Since you're already familiar with Mandl & Wolf's "standard semi-classical" approach (whereas, judging from post 10, Marty's "independent" approach is inspired by only your brief description), could you tell me 1) whether that approach can be correctly characterised as treating the electron according to Schroedinger's eq. and the light as a classical wave, and 2) which tests does the "standard semi-classical" model fail?

No, the Mandl and Wolf's approach does not not claim to be able to derive the work function via first principle. This was never the issue until monish claimed that one can simply GET the work function by looking at the conduction bandwidth, as IF that is something one can do easily via "solving the Schrodinger equation". That is what I questioned. The schrodinger equation one learns in undergraduate QM is inadequate in its simple form to calculate such a thing because this is a many-body problem.

My personal idea here is that, if the answers are 1) yes and 2) none, than it cannot really be correct to argue that the PE implies anything about the nature of light. If (2) has a different answer, I hope to use aspect (2) of the PE as a simple (and honest) example (possibly preferable to Compton scattering and Feynman's observation that photodetectors click discretely) for teaching the existence of photons.

When I used to teach this thing, I never claim that the Photoelectric effect is the de facto evidence for photons. I did say that it presents a strong evidence for photons and historically, the impetus for considering its validity. You will notice on here that I have consistently said so. I also claim that we lose no generalities for saying this because (i) we know that this is the ONLY scenario in which many other photoemission-related phenomena are explained, with absolutely no wave-related explanation and (ii) other types of phenomena such as the which-way experiments, photon antibunching experiments, etc., clearly have no classical wave scenario.

There is very seldom just ONE experiment that is a slam dunk for one particular theoretical description in physics. Can you think of any? I certainly can't. In a superconductor, for example, one just doesn't show that the resistivity goes to zero at some temperature and expect this to be sufficient. The susceptibility measurement and the presence of an energy gap are usually also required for anyone to claim to have discovered superconductivity in any new materials. Therefore, *I* certainly would not go about doing such a thing especially with that knowledge in mind. But I don't see any problem with claiming that the PE is a very strong evidence for photons. With what we already know now, I don't see this being an issue.

Zz.

 

[monish]

Mentor, is your purpose to demonstrate your personal superiority? Since you're already familiar with Mandl & Wolf's "standard semi-classical" approach (whereas, judging from post 10, Marty's "independent" approach is inspired by only your brief description), could you tell me 1) whether that approach can be correctly characterised as treating the electron according to Schroedinger's eq. and the light as a classical wave, and 2) which tests does the "standard semi-classical" model fail?

My personal idea here is that, if the answers are 1) yes and 2) none, than it cannot really be correct to argue that the PE implies anything about the nature of light. If (2) has a different answer, I hope to use aspect (2) of the PE as a simple (and honest) example (possibly preferable to Compton scattering and Feynman's observation that photodetectors click discretely) for teaching the existence of photons.

Exactly. I keep hoping we can move the discussion forward to "aspect 2", but I'm hesitant to bring it up myself until we've got some resolution on "aspect 1".

 

[monish]

You've already misread the posts in here once. You might want to pay a closer attention before you make another accusation.

Are you sure you want to direct this at CesiumFrog? I think I was the one who misread a post earlier.

One can already get the idea of the existence of the work function without knowing any "theoretical" description...The schrodinger equation one learns in undergraduate QM is inadequate in its simple form to calculate such a thing because this is a many-body problem.

I'm going to accept your statement that the simple form of the Schroedinger equation we learned in undergrad school is inadequate to solve for the band structure in a metal. Sometimes I use the phrase "the Schroedinger equation" as a shorthand for "standard qm calculations of the electron wave function". I think this is how they solve for band structures.

What you CAN do at the undergrad level is solve for some simple physical cases like the potential well or the hydrogen atom. Both these cases show clearly how the different energy levels have different frequencies. And when you take superpositions of states with different frequencies, the resultant charge density sometimes oscillates, giving you a classical antenna. This is certainly true for such combinations as the 1s-2p state of the hydrogen atom. Maybe you've seen the applets people have made up of this and posted on the internet? It's also true for some superpositions of bound states with free states.
You can construct some pretty good ones with the potential well. Actually, in the one I'm thinking of, you don't necessarily get oscillating charge; you get surface charge waves traveling faster than the speed of light. This of course is also a valid classical antenna; it's the same kind of charge waves you get when ordinary light falls on a metal sheet at an angle.

These theoretical cases show exactly the type of behavior characteristic of the photo-electric effect experiments. Below the threshold frequency, there is no coupling between the bound states and the free states. Above the theshold frequency, the superposition of these states interacts strongly with radiation. So one state can be driven into the other state.

I know how to get the work function. The question is, DO YOU? You seem to think this is a trivial exercise. It isn't. It requires a band structure calculation that is tied to how the crystal lattice is formed and the valence shell of the atoms making up the solid. It isn't trivial!

So show me how. Please do this in your next post, because this will be the last time I will entertain you avoiding a direct answer to my question.

Zz.

Sometimes we can't do the full-blown calculation on an actual physical system so we do our best with a simplified version. I'm sorry I wasn't able to show you how to calculate the work function. Even so, I still value your input to this discussion and hope you will continue to participate.

 

[ZapperZ]

I'm going to accept your statement that the simple form of the Schroedinger equation we learned in undergrad school is inadequate to solve for the band structure in a metal. Sometimes I use the phrase "the Schroedinger equation" as a shorthand for "standard qm calculations of the electron wave function". I think this is how they solve for band structures.

What you CAN do at the undergrad level is solve for some simple physical cases like the potential well or the hydrogen atom. Both these cases show clearly how the different energy levels have different frequencies. And when you take superpositions of states with different frequencies, the resultant charge density sometimes oscillates, giving you a classical antenna. This is certainly true for such combinations as the 1s-2p state of the hydrogen atom. Maybe you've seen the applets people have made up of this and posted on the internet? It's also true for some superpositions of bound states with free states.
You can construct some pretty good ones with the potential well. Actually, in the one I'm thinking of, you don't necessarily get oscillating charge; you get surface charge waves traveling faster than the speed of light. This of course is also a valid classical antenna; it's the same kind of charge waves you get when ordinary light falls on a metal sheet at an angle.

These theoretical cases show exactly the type of behavior characteristic of the photo-electric effect experiments. Below the threshold frequency, there is no coupling between the bound states and the free states. Above the theshold frequency, the superposition of these states interacts strongly with radiation. So one state can be driven into the other state.

This is wrong. A hydrogen atom has no "work function". It has a ionization potential, but it doesn't have a continuous band that a metal has! The study of solid is not identical to the study of atom and molecules. That's why we have "solid state physics".

You have just shown here that you can't derive the work function. Do you still claim to be in possession of the ability to arrive at the photoelectric effect using QM and classical wave theory? If you do, let's see it explicitly.

Zz.

 

[monish]

You have just shown here that you can't derive the work function.

That's not what I was trying to show. It was you who said that it couldn't be derived from Schroedinger's equation, and I said I was willing to accept your assertion. I don't know if it's true; I'm pretty sure the work function comes out, as I said, from a pretty conventional q-m analysis. I accepted your claim because I thought I could show how the frequency threshold arises naturally from Schroedinger's equation without needing to do an exact calculation of the work function. That's why I used easy examples that would be accessible at the undergrad level.

Do you still claim to be in possession of the ability to arrive at the photoelectric effect using QM and classical wave theory? If you do, let's see it explicitly.

Zz.

I honestly think I did a pretty decent job of explaining the frequency threshold. Which was the main objection to the wave theory that has been raised so far. Is there any other aspect of the experiment you'd like me to try to explain?

Marty

 

[ZapperZ]

I honestly think I did a pretty decent job of explaining the frequency threshold. Which was the main objection to the wave theory that has been raised so far.

You did? I re-read what you wrote and no where is there ANY explanation of it. You used the H-atom, which isn't even close to being anywhere near to even mimic the work function or the photoelectric effect spectrum. Somehow, the fact that the conduction band is continuous, while the H-spectrum is discrete doesn't bother you at all?

I don't know how you could convince yourself that what you are doing here has any agreement with the photoelectric effect.

Zz.

 

[monish]

You did? I re-read what you wrote and no where is there ANY explanation of it. You used the H-atom, which isn't even close to being anywhere near to even mimic the work function or the photoelectric effect spectrum...I don't know how you could convince yourself that what you are doing here has any agreement with the photoelectric effect.

Well, the analogue of the work function in this case would be what I think is called the ionization potential. In the photoionization of hydrogen, you need the minimum frequency before you can drive the transition. In the photo-electric effect, similar idea.

I don't know what you mean about explaining the "photoelectric effect spectrum". If you'd care to clarify this I can try to respond.

Somehow, the fact that the conduction band is continuous, while the H-spectrum is discrete doesn't bother you at all?

Zz.

No, it never bothered me until you mentioned it just now. I'm not sure I see how this makes an essential difference in the relevant physics. In both cases, were coupling from a bound state to a free state. I just find the hydrogen atom (and the potential well) easier to calculate explicitly because the bound state wave function is readily described.

If you can explain why the photo-electric effect is qualitatively different, I'd be interested.

 

[ZapperZ]

Well, the analogue of the work function in this case would be what I think is called the ionization potential. In the photoionization of hydrogen, you need the minimum frequency before you can drive the transition. In the photo-electric effect, similar idea.

I don't know what you mean about explaining the "photoelectric effect spectrum". If you'd care to clarify this I can try to respond.

No, it never bothered me until you mentioned it just now. I'm not sure I see how this makes an essential difference in the relevant physics. In both cases, were coupling from a bound state to a free state. I just find the hydrogen atom (and the potential well) easier to calculate explicitly because the bound state wave function is readily described.

If you can explain why the photo-electric effect is qualitatively different, I'd be interested.

You know what the photoelectric effect is, don't you? Now how are you able to derive QUANTITATIVELY all of that have been observed?

For example, if you look at the energy spectrum of the photoelectrons, you'll see a continuous spectrum of energy. You don't see that in an H-atom spectrum. Not only that, take carbon atoms. Arrange it one way, you get one value of the work function, but arrange it another way, you get ANOTHER diferent value of the "work function". Why? The crystal structure dictates how the valence shell overlaps and by how much. Yet, these are still carbon atoms forming two different material, diamond and graphite. In your example, you'll see discrete spectrum of only ONE type, no matter how you arrange them, because all you care is the isolated energy spectrum. It just doesn't fit the experiment.

And oh, btw, my avatar is one such example of a photoemission spectrum that included both the energy (horizontal axis) and momentum (vertical axis) distribution of the photoelectrons. I can assure you that you DO NOT get this when you look at the ionization spectrum of isolated atoms.

If you think you can derive all of the photoelectric effect using simple QM and wave theory, please submit it for consideration for publication, or to the IR forum. I believe I have seen enough of this to qualify it as speculative, unverified personal theory, which is a violation of our guidelines. If the OP has any followup, he/she may contact me to have this thread reopened.

Zz.