Talk:Orbital angular momentum of electron vortex beams

Single electron vs. electron beam

MaoGo, it looks like you got some bad information on the Wikiproject:Physics talk page, so I want to clarify the question of whether a single electron can carry orbital angular momentum. This is clear from the fact that the orbital angular momentum operator projected along the propagation direction, $L_{z}$ and the free space Hamiltonian, $H_{free}$, commute. Free electron states can therefore be written as eigenstates of both $L_{z}$ and energy. The work of Konstantin Bliokh (https://doi.org/10.1016/j.physrep.2017.05.006) is very helpful for understanding this and similar foundational points regarding electron OAM.Tyharvey313 (talk) 11:50, 2 July 2018 (UTC)

@Tyharvey313:Please do not move the page without discussion. May you clarify with an actual quote from the article(s) if you may have a single electron with angular momentum projected in the propagation direction. If it is not the case I find it misleading to not clarify it correctly in the article. --MaoGo (talk) 12:41, 2 July 2018 (UTC)

Also the title problem is still not solved. Is this article about the orbital angular momentum of electrons with respect some point in the lab or free electron model electrons in a metal? I still think the best title is 'Electron vortex beams. --MaoGo (talk) 13:38, 2 July 2018 (UTC)

I can't immediately find any direct quotes where somebody specifies 'single electron', but that's implicit in the formalism used in, for example, the 2007 Bliokh paper now referenced in the article. The closest I can find to a direct quote is this section header in that paper (https://doi.org/10.1103/PhysRevLett.99.190404): 'OAM states of a free electron'. I agree that this should be clarified in the article. I've invited a few other researchers in this field who I think could add a lot to this article to contribute to it. Hopefully somebody bites soon. I can do it eventually if no one else does, but I think the article will be a lot better if others add more to it. Your question regarding whether the article is about electrons in vacuum or in a metal is an important one, but the answer is that it doesn't matter. The papers cited all consider electrons in vacuum, because it's easier to control electron wavefunctions there. In fact, several papers have shown that there are Landau levels for electrons in vacuum in a magnetic field (https://doi.org/10.1103/PhysRevX.2.041011,https://doi.org/10.1038/ncomms5586). So, all the dynamics that can be observed in vacuum can be observed, to the degree that technology allows and as far as the free-electron model holds, also in a metal. There have also been a few papers that consider the conservation of OAM in crystals for TEM-energy electrons (https://doi.org/10.1017/S1431927612000499,https://doi.org/10.1107/S0108767312013189). The slow changes in OAM that they predict would be exaggerated for an electron near the Fermi level, but the general considerations hold. I hope we can get all of this into the article eventually! I would personally be fine with Electron vortex beams, but as electron vorticies and optical vorticies are parallel topics, I think it's good to keep the names consistent. It looks like they had a long discussion over at Talk:Orbital_angular_momentum_of_light#Requested_move and the consensus was Orbital angular momentum of light. For some strange reason Optical vortex and Vortex laser beam also exist, but both are shorter than Orbital angular momentum of light (actually, I just proposed a merge of all those pages, because they all have the same scope). I think we should keep a parallel name here with whatever results from that merge. Tyharvey313 (talk) 17:47, 2 July 2018 (UTC)

The change is wrong. The original title Orbital angular momentum of free electrons is correct. Xxanthippe (talk) 03:38, 21 July 2018 (UTC).