标题： 利用时变运动常量求解薛定谔方程 显示英文标题

标题： Solution of the Schrödinger equation making use of time-dependent constants of motion

摘要： 结果表明，如果由运动常量构成一组完全的相互对易算符，则直到仅依赖于时间的一个因子为止，这些算符的公共本征函数都是薛定谔方程的解。 特别地，表示粒子笛卡尔坐标初始值的算符是彼此对易的运动常量，从它们的公共本征函数可以很容易得到格林函数。 显示英文摘要

摘要： It is shown that if a complete set of mutually commuting operators is formed by constants of motion, then, up to a factor that only depends on the time, each common eigenfunction of such operators is a solution of the Schr\"odinger equation. In particular, the operators representing the initial values of the Cartesian coordinates of a particle are constants of motion that commute with each other and from their common eigenfunction one readily obtains the Green function.