曲面上的动量和动能算符

对约束在曲面上粒子运动的描述可以在内部坐标即曲面局部坐标下进行，也可以在外部坐标即在笛卡尔坐标下进行.在量子力学中，动量和动能算符的表示在这两种描述中各有不同，前者的动量算符仅包含内禀几何量，后者的动量算符包含了曲面的平均曲率.考虑到算符次序问题，动能算符对动量算符的依赖关系也不同，前者的依赖关系仅发现存在一种，后者的依赖关系已经发现有两种. 关键词： 量子力学 微分几何

The Cartesian momentum and the kinetic operators on curved surfaces

For describing particles moving on the two dimensional curved surfaces, we can use either the intrinsic local coordinates or the Cartesian coordinates. The representation of the momentum operators differs from each other in these two kinds of coordinates, the former ones depend on the intrinsic geometrical quantities, but the latter case depend on a geometrical invariant, namely the mean curvature. Taking the operator-ordering problem into consideration, the kinetic operator for the former case can be expressed in a possibly unique way, while that for latter case can be expressed in two different ways.