论文标题
在非均匀磁场中的电子涡流梁
Electron vortex beams in non-uniform magnetic fields
论文作者
论文摘要
我们考虑在非均匀磁场（例如Glaser场）中近后非相关电子束的量子理论。我们从这样的光束中发现电子的波函数，并表明它是两个（$ z $依赖性的）通勤量规依赖性运算符的联合本征态。这种广义的拉瓜仪式涡流梁具有一个相显示的相位，该相显示由两个部分组成，每个部分都与两个保守的操作员之一的特征值成正比，每个值都具有不同的对称性。我们还描述了任何模式的角动量和横截面区域的动力学，以及变化的磁场如何将模式分为模式的叠加。通过适当的改变，我们的所有分析也适用于具有时间依赖磁场的量子霍尔系统中的电子。
We consider the quantum theory of paraxial non-relativistic electron beams in non-uniform magnetic fields, such as the Glaser field. We find the wave function of an electron from such a beam and show that it is a joint eigenstate of two ($z$-dependent) commuting gauge-independent operators. This generalized Laguerre-Gaussian vortex beam has a phase that is shown to consist of two parts, each being proportional to the eigenvalue of one of the two conserved operators and each having different symmetries. We also describe the dynamics of the angular momentum and cross-sectional area of any mode and how a varying magnetic field can split a mode into a superposition of modes. By a suitable change in frame of reference all of our analysis also applies to an electron in a quantum Hall system with a time-dependent magnetic field.
