均匀磁场的耦合曲率：解析和数值研究
Coupling curvature to a uniform magnetic field; an analytic and numerical study
摘要：
本文导出了在任意均匀磁场$\mathbf B$作用下，方位对称曲面$Σ$附近电子的薛定谔方程。一个薄层量子化过程的实施，使电子到$Σ$上，导致众所周知的几何势$V_C \propto h^2-k$和第二个潜在的耦合$A_N$，$\mathbf A$垂直于$Σ$平均表面曲率的组成部分，以及一项依赖于$Σ$上评估的$A_N$的正常导数。数值结果的形式的基态能量作为一个功能的应用领域在几个方向上的环形模型。
英文摘要：
The Schrodinger equation for an electron near an azimuthally symmetric curved surface $Σ$ in the presence of an arbitrary uniform magnetic field $\mathbf B$ is developed. A thin layer quantization procedure is implemented to bring the electron onto $Σ$, leading to the well known geometric potential $V_C \propto h^2-k$ and a second potential that couples $A_N$, the component of $\mathbf A$ normal to $Σ$ to mean surface curvature, as well as a term dependent on the normal derivative of $A_N$ evaluated on $Σ$. Numerical results in the form of ground state energies as a function of the applied field in several orientations are presented for a toroidal model.
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