Undergrad How quickly do electrons jump orbitals?

[PeroK]

Yes, well in introductory (and non relativistic) QM texts you read quite often "The wave function of a particle is ..." or "The wave function of a particle has this property..." so you easily can form the false impression that all the particles can have wave function.

Good old Griffiths leaves the reader in no doubt:

The photon ... is a relativistic object if ever there was one, and therefore outside the scope of non-relativistic QM. It will be useful in a few places to speak of photons ... but please bear in mind that this is external to the theory we are developing.

 

[vanhees71]

I mean the usual wave function. The electron as a particle has a wave function, the photon which also is a particle (not in the usual sense though) must have a wave function as well shouldn't it?

The electron as a particle has a wave function in the non-relativistic limit. What really makes relativistic QT different from non-relativistic QT is that in interactions of "particles" there's always the possibility to create new particles and/or destroy particles. That's why a single-particle wave function for an interacting particle can at best be an approximation. What you need is some description that allows to take the creation and destruction of particles into account, and the most convenient way is quantum field theory. That's why relativistic QT nowadays is formulated as local relativistic QFTs.

Massless "particles" are special in the sense that they have no non-relativistic limit, and that's because there's no "mass gap" to overcome to create them. E.g., even at the lowest collision energies of charged particles or of photons with charged particles there's always the possibility to create "soft photons" ("Bremsstrahlung").

Also formally massless particles do not make sense in non-relativistic quantum mechanics, because the representations of the quantum version of the Galileo group with $m=0$ don't lead to a physically sensibly interpretable dynamics.

Last but not least, for the photon as a massless particle with spin $1>1/2$ you cannot define a position observable in the usual sense. So it is already impossible to formulate a single-photon wave function to begin with.

 

[Grasshopper]

This article is not standard QM; it is a speculative hypothesis by the author.

Hopefully not full on crackpottery though, because yeah I’d be pretty upset and disappointed in the brands involved (which are supposedly reputable).

Anyway, it appears that the question in the context of established quantum mechanics is like asking what the color of middle C is (e.g., entirely meaningless). It is unfortunate there is a disconnect of this nature between QM and classical physics, but it’s not like I’m in position to understand a potential breakthrough on that front anyway.

 

[PeterDonis]

The electron as a particle has a wave function

In non-relativistic QM, yes.

, the photon which also is a particle (not in the usual sense though) must have a wave function as well shouldn't it?

No, because there is no non-relativistic model of a photon; they are inherently relativistic.

 

[Delta2]

Is photon the only particle of the standard model that doesn't have a wave function or there are others too, for example an electron having relativistic speed doesn't have a wave function either?

 

[PeterDonis]

Is photon the only particle of the standard model that doesn't have a wave function

It's not a matter of "which particle". It's a matter of whether you are using a non-relativistic or relativistic model. The standard model itself is a relativistic model--it's a quantum field theory--so a correct statement would be that no particles in the standard model have wave functions. To get wave functions at all, you have to work in the non-relativistic limit, which means you're not really using the standard model any more.

As for which particles can have a non-relativistic limit, only particles with nonzero rest mass can.

an electron having relativistic speed doesn't have a wave function either?

Correct, since you can't model it in the non-relativistic limit.

 

[vanhees71]

To the contrary! QM connects to nature better than classical physics, which is an approximation. Without QM there'd not be stable matter

Is photon the only particle of the standard model that doesn't have a wave function or there are others too, for example an electron having relativistic speed doesn't have a wave function either?

In principle for any massive particle you can use a non-relativistic approximation, and non-relativistic quantum mechanics can be described in terms of a wave function (Schrödinger's wave mechanics). As I tried to explain above, such an approximation is valid if the involved interaction/collision/binding energies are small compared to all masses (times $c^2$) of the particles involved in your description. If this is not the case and if not other conservation laws prevent the production and/or annihilation of particles, you need to use QFT to deal with these production and annihilation processes.

Massless particles do not have a relativistic limit. It's well known that the assumption of zero mass does not lead to a representation of the Galileo group that has a sensible physical interpretation as a quantum theory.

 

[Delta2]

Hmm let me see, is
Relativistic QM=QFT or
QFT is something even more?

 

[vanhees71]

There is no relativistic QM beyond the quasi-nonrelativistic approximations.

QFT is the most general framework for all kinds of quantum theory. You can describe usual non-relativistic quantum mechanics also in terms of a non-relativistic QFT. It's known as "second quantization", because formally you get it by "quantizing the Schrödinger field", but that's a misnomer, because it's just the same non-relativistic quantum mechanics just expressed in a different way.

Now, since QFT is a more general framework, there are physical situations, where you can use QFT but not QM. That's always the case if you don't deal with a fixed conserved number of particles but with creation and annihilation processes, and that's the case in relativistic quantum theory, because you always there's some chance to create and destroy particles in scattering processes at relativistic energies.

Even in non-relativistic theory you can have such cases, if it comes to the description of condensed matter. There you often can describe complicated phenomena by socalled quasi-particles. This technique was ingeniously discovered by Landau. There you describe excitations of a condensed-matter system (usually assumed to be close to thermal equilibrium) by quasiparticles. These are not real particles, but the math of the usually non-relativistic QFT looks right the same. An example are the oscillations of a solid, which are nothing else than sound waves. These you can describe by quasiparticles which are rightfully named "phonons". These can be destroyed and created and thus must be described by a (in this case non-relativistic) QFT.