球谐函数的动量谱及几何嵌入效应的探讨
Momentum spectrometry of spherical harmonics and a probe of geometric embedding effect
摘要：
当一个子流形被嵌入到高维平坦空间中时，量子力学给出了各种嵌入量，例如，对于在二维球面上运动的粒子或自由旋转的球顶，几何动量p和角动量L在某个笛卡尔坐标轴上的投影构成一组完备的可交换观测量[ p_{i}，L_{i} ]=0（i= 1，2，3）.因此，我们有二维球面上的状态的（p_{i}，L_{i}）表示。自由转动刚性转子的基态的几何动量分布在现有动量谱仪的分辨能力范围内，可以通过测量来探测嵌入效应。
英文摘要：
As a submanifold is embedded into higher dimensional flat space, quantum mechanics gives various embedding quantities, e.g., the geometric momentum and geometric potential, etc. For a particle moving on a two-dimensional sphere or a free rotation of a spherical top, the projections of the geometric momentum p and the angular momentum L onto a certain Cartesian axis form a complete set of commuting observables as [p_{i},L_{i}]=0 (i=1,2,3). We have therefore a (p_{i},L_{i}) representation for the states on the two-dimensional spherical surface. The geometric momentum distribution of the ground states for a freely rotating rigid rotor seems within the resolution power of present momentum spectrometer and can be measured to probe the embedding effect.
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