经典系统的量子化

ON THE QUANTIZATION OF CLASSICAL SYSTEMS

用几何语言扼要阐述了有限自由度无约束经典系统量子化的普遍理论，着重介绍动量变量的准确定义及动量算符的一般表式，证明了动量算符表式中附加散度项对保证厄米性的重要作用；并以此为指导对量子力学教学界长期存在的“正则动量算符之争”给出明确结论，同时也澄清了与量子化有关的若干重要认识问题。

The quantization theory of classical systems having a finite number of degrees of freedom and having no constraints is described in geometrical language.The emphasis is placed on the exact definition of momentum variables and the general expression of momentum operators, and the importance of the additional divergence term in this expression to ensuring their hermiticity is demonstrated. Under the guidance of this theory, the long-standing controversy about momentum operators is given a clear -cut conclusion, and certain issues related to quantization are clarified.