Lamb and The Photoelectric Effect Without Photons

[A. Neumaier]

Again, what is "quantized" for the conduction BAND?! This is a continuum energy states!

The rest of your post continues to perpetuate the faulty idea that the photoelectric effect is done on isolated atoms, which it is not! Photoionization is not the same as the photoelectric effect. If you truly think that it is the material that's responsible, then pay attention to the physics of the material!

There are free effective electrons in the conduction band and there are effective electrons that are loosely bound. Each of these is reasonably localized. It is the latter that behave as more or less independent qubits, since they can get excited to the energy of the conduction band. And only this counts for the photoeffect. The effect is not much different if one adds more complexity to the quantum mechanical model of the material - only the calculations become far more complex. In all applications of quantum mechanics, one simplifies the model to such an extent that, while the essential point is modeled precisely, everything else is neglected as far as possible.

If you think that this is not good enough, then please point to _any_ explanation of the photoeffect involving conduction electrons that satisfies you, so that I can see what you'd consider satisfactory.

There is also a recent related thread:
https://www.physicsforums.com/showthread.php?t=474537

 

[Iuval]

Classical EM field already quantized

Perhaps we can take the view that the classical electromagnetic field can already be cast in the form of a quantum wave function (PROGRESS IN OPTICS XXXVI, pp. 245-294
E. WOLF, Editor, Elsevier, Amsterdam, 1996, photon wave function, by Iwo Bialynicki-Birula). I have only recently become aware of this quite radical statement. Apparently Oppenheimer was already aware of it in 1931. There is no localization of photons in this view (can't define a postion operator for a highly relativistic particle of spin 1), but there is a possible localization of photon energies. The wave function is related to the positive frequencies of E+iB. I don't think this is quite correct because a macroscopic classical field is really a superposition of many body photon states. In this view, second quantization is a misnomer. You can't quantize what is already quantized, namely a wavefunction/EM field. You can however develop a sophisticated way of treating a many body system of bosons and/or fermions where the number of them is not necessarily conserved, and that is all second quantization is. There is no "wavefunctional" of the classical electromagnetic field.

So the main difference relevant here between photons and electrons is that the wave nature of electrons was not known until quantum mechanics, whereas the wave nature of photons was already known before quantum mechanics (which might at a deeper level be due to the statistical properties of fermions vs bosons). What was not known about photons before quantum mechanics is that under certain conditions they can be considered as having a well defined momentum and localized energy, which makes them particle-like. Also the fact that for a fixed frequency there is a minimum energy (hv) for the wave (consisting of one photon), and also the statistical description that a wavefunction provides for obtaining transition amplitudes, average values of measurables, etc. But this is obvious from the quantum theory. The particle description, without reference to the classical em field or equivalently the quantum wavefunction of the many photon system is less complete.

 

[Cthugha]

Welcome to these forums.

This thread has been dead for a while. If you are interested in ways to think about photon wavefunctions, you might find John Sipe's work on that of interest (Phys. Rev. A 52, 1875–1883 (1995), http://pra.aps.org/abstract/PRA/v52/i3/p1875_1).

However, I disagree with some of your claims. The photon is NOT perfectly localized in the standard particle picture (The Mandel/Wolf has a short chapter on why you cannot localize photons too far) and I do not see why the particle description is less complete. In the quantum optics picture, the meaning of the photon as a particle is that it is the excitation of a field, so if you want to discuss particles, you also discuss fields.

 

[Iuval]

If you are interested in ways to think about photon wavefunctions, you might find John Sipe's work on that of interest (Phys. Rev. A 52, 1875–1883 (1995), http://pra.aps.org/abstract/PRA/v52/i3/p1875_1).

That paper was referenced in the review article I referenced and read, so probably nothing new.

The photon is NOT perfectly localized in the standard particle picture (The Mandel/Wolf has a short chapter on why you cannot localize photons too far)

I did not say the photon can be perfectly localized, but that one can associate a localized energy with it. I haven't investigated the details of why the latter claim is so (I have however investigated a bit the details of what you thought I was saying), and this is one of the claims made in the review paper.

I do not see why the particle description is less complete.

Because a particle is a classical concept, and the world, at least as far as we know (some people, including myself are trying to recast quantum mechanics in a classical paradigm at a deeper level, but that is another story), is quantum mechanical, where there are no particles or waves, but particle/waves described by wave functions or equivalently operators.

in the quantum optics picture, the meaning of the photon as a particle is that it is the excitation of a field, so if you want to discuss particles, you also discuss fields.

I don't disagree with you, but I think this is an extremely strange thing that probably means something deeper that we have missed. Here is why: we can start with a quantum object, the photon particle/wave. It has a wave function which is roughly E+iB, which means everything we want from a wavefunction except localization in position space. Now because of the symmetry of many photon wavefunctions, a macroscopic classical field emerges when we have many photons. But this is sort of chimera. The real object is the wavefunction. However, if we forget that and "quantize" this classical chimera (which is nonsense since a wavefunction is already quantized), we get a bunch of independent harmonic oscillators in momentum space, with eigenenergies equal to the energies of a discrete number of photons. So based on the eigenenergies we (prematurely?) say that the photons are the excitations of the classical EM field. But the photons are not, as far as I know, Hermite polynomial wave functionals in the classical field (times a time dependent complex exponential), which are the solutions to the functional Schrodinger equation.

We don't get into this sort of trouble with fermions because there is no classical field emerging out of the many particle wavefunction (sorry, but Grassmanian fields have not been observed, not only because they are not Hermitian, but because they don't exist except in the minds of mathematicians).