中心力场中的电子涡旋

Electron vortices in the central field

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.

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.