华东师范大学学报(自然科学版) ›› 2023, Vol. 2023 ›› Issue (4): 151-163.doi: 10.3969/j.issn.1000-5641.2023.04.016

• 物理学与电子学 • 上一篇    下一篇

中心力场中的电子涡旋

周永香1, 薛迅1,2,3,*()   

  1. 1. 华东师范大学 物理与电子科学学院, 上海 200241
    2. 新疆大学 理论物理中心, 乌鲁木齐 830046
    3. 华东师范大学重庆研究院, 重庆 401120
  • 收稿日期:2022-04-08 出版日期:2023-07-25 发布日期:2023-07-25
  • 通讯作者: 薛迅 E-mail:xxue@phy.ecnu.edu
  • 基金资助:
    国家自然科学基金(11775080, 11865016); 重庆市自然科学基金(CSTB2022NSCQ-MSX0351)

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 E-mail:xxue@phy.ecnu.edu

摘要:

电子涡旋波最早是在轨道角动量守恒的系统中被发现. 对于轨道角动量不守恒的系统, 涡旋波的存在与否尚不清楚. 以相对论情况下的中心力场中的电子为例, 构建了在轨道角动量不守恒但总角动量守恒的情况下, 当携带固定总角动量的电子沿 $z$ 轴传播时, 对此时系统所对应的电子涡旋波进行微扰求解; 并结合Foldy-Wouthuysen (F-W)变换, 说明了在相对论情况下, 中心力场下携带轨道角动量的电子沿 $z$ 轴传播时确实存在涡旋解, 同时展示了相对应的涡旋波解和螺旋等相位面.

关键词: 相对论电子涡旋波, 中心力场, Foldy-Wouthuysen (F-W) 变换, 轨道角动量

Abstract:

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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