不同坐标系中的正则量子化要求

Requirements of the Canonical Quantization in Different Coordinates

阐明了在利用正则对易关系[^qi,^pj]=iδij得到^qi和^pj的具体表达式时,必须同时考虑^pj的厄米性要求,为了得到在非笛卡儿坐标系中的正确的哈密顿算符 ,总是从笛卡儿直角坐标系出发找出 ,再通过坐标变换关系将笛卡儿坐标系中的 变换到所需要的非笛卡儿坐标系.

This article illustrates that when we get the formula of _i&_j from canonical commutation rules _i,_j=iδ_(ij),we must take into account at the same time the Hermiticity of _j.To get the right quantum Hamiltonian operator  in non-Cartesian coordinates,we always need to change  in Cartesian coordinates into non-Cartesian coordinates by using the coordinates transformation.