经典粒子和量子微观粒子的运动轨道

MOVING PATHS FOR A CLASSICAL PARTICLE AND A MICROSCOPIC PARTICLE

用量子力学传播子讨论了经典粒子和量子微观粒子沿着不同轨道对传播子的贡献 .通过这样的计算可以清楚地看到为什么经典粒子只是沿着满足最小作用原理的轨道 ,即经典轨道运动 ,而对于量子微观粒子沿着许多条路径都有可能 .这篇短文将一些教科书中的讨论用具体的数学表达出来 ,使得读者更容易理解 .计算表明 ,对于质量较大的经典粒子 ,沿着非经典轨道对传播子的贡献和它周围的临近轨道有强烈的抵消 .只有在经典轨道附近对传播子的贡献才不为零 .对于量子微观粒子没有这种差别 。

In this note,we calculated the propagator for a classical particle and a microscopic particle,respectively.We discussed how a classical particle takes only the path that the least action principle allows while for a quantum particle all paths contribute.By careful calculation,we find that for a classical particle,the contribution to the propagator from a non\|classical path interferes destructively with other paths in its vicinity and hence does not contribute to the propagator.While for a quantum particle,this does not happen,all paths contribute to the propagator.