笛卡尔动量算符的约束诱导平均曲率依赖性
Constraint-induced mean curvature dependence of Cartesian momentum operators
摘要：
本文证明了在$R^{3}$中嵌入表面$M$的厄米笛卡尔量子动量算符$\mathbf{p}$是一个常数因子$-i\hbar $乘以平均曲率向量场$H\mathbf{n}$加上通常的微分项.使用这种形式的动量算符，在构造正确的动能算符时存在算符排序模糊性，并且三种不同的算符排序会导致相同的结果。PACS：03.65。w量子力学，04.60.Ds正则量子化
英文摘要：
The Hermitian Cartesian quantum momentum operator $\mathbf{p}$ for an embedded surface $M$ in $R^{3}$ is proved to be a constant factor $-i\hbar $ times the mean curvature vector field $H\mathbf{n}$ added to the usual differential term. With use of this form of momentum operators, the operator-ordering ambiguity exists in the construction of the correct kinetic energy operator and three different operator-orderings lead to the same result. PACS: 03.65.-w Quantum mechanics, 04.60.Ds Canonical quantization
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