空间平移不变性与动量守恒的严格证明

An Exact Derivation of Conservation of Momentum for Quantum System Under Invariance of Translation in Space

动力学系统的对称性与守恒量研究有着深远的意义 ,由时空对称性导出的能量、动量等守恒定律是跨越物理学各个领域的普遍法则。对于量子系统守恒量的推导 ,一般文献资料及教材多采用对时空坐标作无限小变换 ,并对波函数作一阶近似展开和借助Lie对称性而推出相应的守恒量。本文从Schr¨odinger绘景出发 ,并对空间平移变换下的波函数作完全的级数展开 ,借助Lie对称性而导出动量守恒。较之仅作一阶近似展开的文献资料和著作的证明更为严谨。

Symmetry in space and time lead to the conservation laws of energy and momentum,which are a general principle across all fields of physics So.it is of great importance to study symmetrization and conservation laws of mechanical system,While in most of general literatures and textbooks the derivations of conservation of momentum for quantum systems are made by infinitesimal translations in space,by approximate expansion of wave functions as the first order,or by means of the Lie symmetries.In this paper,the conservation of momentum is derived from the picture Schrdinger and the wave functions belonging to the translations in space are made to expand in power series and with the help of Lie symetries,the conservation of momentum is obtained.It is more precise than that in the literatures.