There is a recent publication in PRL (Feb. 2014) by Schmidt et al., which says that there are vortices associated with the wave function of a single electron. Their abstract is as follows: "We present measurements and calculations of the momentum distribution of electrons emitted during the ion-atom collision ... which show rich structures for ion scattering angles above 2 mrad arising dominantly from two-electron states. Our calculations reveal that minima in the measured distributions are zeros in the electronic probability density resulting from vortices in the electronic current." (ref. http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.083201, or see: http://arxiv-web3.library.cornell.edu/pdf/1402.6853.pdf).
This paper reminds me to Kobayashi and Shimbori's paper (2001) suggesting that there is vortex solution of Schrodinger equation. (ref. http://arxiv.org/pdf/cond-mat/0103209.pdf).
Can vortices be associated with the wave function of electron?
Thank you, Oscar, for your answer. Does it mean that it is possible to find a realistic meaning of the quantum wave function? Best wishes
See http://www.ncbi.nlm.nih.gov/pubmed/21233382 for a report of creating vortex states of free electrons in an electron microscope, with orbital angular momenta up to 100 \hbar . These correspond to familiar solutions of the Schroedinger equation in polar coordinates; there is also a rich literature on similar solutions of the Maxwell equations i.e. photons with orbital angular momentum. Now, one can quibble about the analogy with vortices in superfluids, where the effects of particle interaction become dominant. But the presence of such structures is generic in systems described by the usual sort of wave equation.
@Victor Christiano
Notice that the current of probability, as a functional of the wave function is homogeneous of the second degree. So, the fact that its curl is not zero identically does not, necessarily, means that the wave functions correspond to physical entities. Vorticity, however plays a fundamental role in mechanics that is not widely recognized. In Hamilton-Jacobi theory you deal with a field of four momentum which is the gradient of the action and, therefore, in the absence of magnetic fields it has zero vorticity. However, if a magnetic field is present, the vector potential is not zero and the kinetic momentum is the canonical momentum minus q A. In that case the field of kinetic momentum has a vorticity. I wrote something in this area a some years ago but I gave up trying to publish it, because it's not main stream and, as a consequence, not suitable for publication. http://arxiv.org/abs/quant-ph/0409012
@Charles. Thank you for your answer. Can you please kindly cite a paper discussing vortice solution of maxwell equations? Thanks
@Oscar. Thank you, i will read your paper Your argument reminds me to a paper long time ago by Prof. Robert M. Kiehn, where he discusses that quantum wave function can be interpreted as vorticity. But that will imply a hydrodynamics/navier-stokes interpretation of quantum mechanics. Do you think that such an interpretation is also possible? Thanks
You can find a lot of work on optical vortices at https://www.researchgate.net/profile/Miles_Padgett/
@Victor Hydrodynamic models of quantum mechanics were proposed a long time ago. arXiv.org > quant-ph > arXiv:quant-ph/0206051
Search or Article-id
(Help | Advanced search)
@Charles. Thank you for the link, yes i find many papers of Dr. Miles Padgett. Can you suggest one paper which clearly discusses vortices, especially associated to wave function? Thanks
@Oscar. Thanks, I will read your paper. best wishes
Dear Oscar, I just tried to download your paper http://arxiv.org/abs/quant-ph/0206051, but there is no pdf file there. Could you please send me the pdf version? Thanks
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Quantum Physics
- Quantum Mechanics