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在轨道角动量守恒的无自旋-轨道耦合系统中存在带轨道角动量量子数的电子涡旋波解, 研究了存在自旋-轨道耦合, 轨道角动量不守恒的系统, 发现携带总角动量量子数的电子旋量波函数也有涡旋波解, 表现为自旋波函数和涡旋波波函数的纠缠波函数. 以中心力场中的电子为例, 构建了自旋-轨道耦合导致的轨道角动量不守恒但总角动量守恒的情况下, 携带固定总角动量量子数的电子沿
$z$ 轴传播的涡旋波旋量波函数结构. 对自旋-涡旋纠缠中相应的电子涡旋波进行了微扰求解, 并结合Foldy-Wouthuysen变换, 说明了在相对论情况下, 中心力场中携带固定总角动量量子数的电子沿$z$ 轴传播时也确实存在四分量旋量的涡旋解, 从而为有自旋-轨道耦合导致的轨道角动量不守恒但总角动量守恒的系统提供了存在涡旋结构的理论支持.-
关键词:
- 相对论电子涡旋波/
- 中心力场/
- Foldy-Wouthuysen变化/
- 自旋-轨道耦合
There exists an electron vortex solution with orbital angular momentum quantum in a non-spin-orbit coupling system which has nonconservative orbital angular momentum. We discuss the system with spin-orbit coupling and nonconservative orbital angular momentum, and we can find that the electrons with the total angular momentum numbers also have vortex beam solutions. And the vortex beam is expressed as an entangled wave function of the spin wave function and the vortex wave function. Taking the electrons in the central force field for example, in this paper constructed is a spinor vortex structure which is caused by the propagation of electrons carrying a fixed quantum number of total angular momentum along the z-axis. The spinor vortex structure is under the condition that the orbital angular momentum caused by spin-orbit coupling is non-conserved but the total angular momentum is conserved. The corresponding electron vortex beams in spin-vortex entanglement are solved by perturbation method, and the Foldy-Wouthuysen transformation is utilized to show that the vortex solution of the four-component spinor does exist in the case of relativity, when the electron with a fixed total angular momentum quantum number propagates along the z-axis in the central force field. The spinor provides theoretical support for the existence of the vortex structure for the system where the orbital angular momentum is not conserved but the total angular momentum is conserved due to spin-orbit coupling.-
Keywords:
- relativistic electron vortices/
- central potential fields/
- Foldy-Wouthuysen transformation/
- spin-orbit coupling
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