稳态action到薛定谔方程的统计偏差
Statistical deviation from stationary action to Schrödinger equation
摘要：
本文在假设哈密顿定态作用原理不精确的基础上讨论了单粒子动力学。然后，我们假设，从平稳动作的足够短的时间间隔的动作的偏差是沿着足够长的轨迹，根据指数律分布。我们证明了，如果平均偏差由$\hbar/2$给出，并且如果两个相反的偏差符号发生的概率相等，则轨迹系综的动力学满足波函数玻恩解释的薛定谔方程。因此，粒子的行为就好像它是由满足薛定谔方程的虚波引导的。
英文摘要：
We discuss the dynamics of single particle by laying a hypothesis that the Hamilton's principle of stationary action is not exact. We then postulate that the deviation of the action with sufficiently short time interval from the stationary action is distributed along a sufficiently long trajectory according to an exponential law. We show that the dynamics of the ensemble of trajectories satisfies the Schrödinger equation with Born interpretation of wave function if the average deviation is given by $\hbar/2$ and if two opposite signs of deviation occur equally probably. The particle thus behaves as if it is guided by a virtual wave satisfying the Schrödinger equation.
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