论文标题
Landau级别和在狭窄空间中的规格不变性问题
Landau Levels and the Issue of Gauge Invariance in Confined Spaces
论文作者
论文摘要
我们在存在磁场的情况下检查了带电粒子在二维限制电势中的行为。限制可以消除原本无限的堕落性，但需要其他成分才能产生明智的结果。我们同时处理圆形和方形的几何形状，在后者中，我们明确证明了能级和波功能振幅的规格不变性。检查了散装状态和边缘状态，在后一种情况下，具有足够高的量子数，我们在正方形和圆形几何形状上有显着差异。使用直接的矩阵力学以一种现场的新手可以访问的方式来实现结果。
We examine the behaviour of a charged particle in a two-dimensional confining potential, in the presence of a magnetic field. The confinement serves to remove the otherwise infinite degeneracy, but additional ingredients are required to produce sensible results. We treat both circular and square geometries, and in the latter we explicitly demonstrate the gauge invariance of the energy levels and wave function amplitudes. Both bulk states and edge states are examined, and in the latter case, with sufficiently high quantum numbers we achieve significant differences in the square and circular geometries. Results are achieved using straightforward matrix mechanics, in a manner that is accessible to novices in the field.
