When a two-dimensional curved surface is conceived as a limiting case of a curved shell of equal thickness d, where the limit d\rightarrow0 is then taken, the well-known geometric potential is induced by the kinetic energy operator, in fact by the second order partial derivatives. Applying this confining procedure to the momentum operator, in fact to the first order partial derivatives, we find the so-called geometric momentum instead. This momentum is compatible with the Dirac's canonical quantization theory on system with second-class constraints. The distribution amplitudes of the geometric momentum on the spherical harmonics are analytically determined, and they are experimentally testable for rotational states of spherical molecules such as C_{60}.
Pauli equation for a charged spin particle on a curved surface in an electric and magnetic field
本文导出了电磁场中自旋带电粒子在空间曲面$\mathcal{S}$上运动的泡利方程。利用薄层量子化方案将粒子约束在$\mathcal{S}$上，在变换后的旋量表示中，我们得到了著名的几何势$V_g$和$e^{-iφ}$的存在，它可以通过曲线坐标导数产生加性自旋连接几何势，并且我们发现文献[Giulio Ferrari and Giampaolo Cuoghi，Phys. Rev. Lett. 100，230403（2008）.]在没有垂直于$\mathcal{S}$的源电流的本系统中仍然有效。最后，我们将表面Pauli方程应用到球面、柱面和环面上，得到了预期的几何势和新的自旋连接几何势，并发现这些方程中只出现正规Pauli矩阵。
Geometric speed limit of state preparation and curved control spaces
Freie Universität Berlin（柏林自由大学）；Nordita, Stockholm University and KTH Royal Institute of Technology（诺迪塔，斯德哥尔摩大学和瑞典皇家理工学院）；Department of Materials Science and Applied Mathematics, Malmö University（马尔默大学材料科学与应用数学系）
