Journal of East China Normal University(Natural Science) ›› 2023, Vol. 2023 ›› Issue (4): 151-163.doi: 10.3969/j.issn.1000-5641.2023.04.016

• Physics and Electronics • Previous Articles     Next Articles

Electron vortices in the central field

Yongxiang ZHOU1, Xun XUE1,2,3,*()   

  1. 1. School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
    2. Center for Theoretical Physics, Xinjiang University, Urumqi 830046, China
    3. Chongqing Institute of East China Normal University, Chongqing 401120, China
  • Received:2022-04-08 Online:2023-07-25 Published:2023-07-25
  • Contact: Xun XUE


Electron vortex beams were first discovered in systems that have a conservable orbital angular momentum; for systems where orbital angular momentum is not conserved, the existence of the electron vortices is uncertain. This article takes the electrons in the central field as examples and, in case of relativity, constructs a case where the orbital angular momentum is not conserved while the total angular momentum is conserved. When the electrons that carry a fixed total angular momentum propagate along the z-axis, the perturbation solution of the electron vortex beams corresponding to the system at this time is calculated and combined with the Foldy-Wouthuysen (F-W) transformation. Accordingly, we can prove, in the case of relativity central field, that the vortex solution does exist when the electrons with orbital angular momentum propagate along the z-axis. Consequently, the corresponding vortex wave solution and spiral isophase surface are shown in this article.

Key words: relativistic electron vortices, central field, Foldy-Wouthuysen (F-W) transformation, orbital angular momentum

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