量子牛顿定律下的轨道
Trajectories in the Context of the Quantum Newton's Law
摘要：
在本文中，我们把最近在量子力学的轨道表象中建立的一维量子运动定律应用于常势、线性势和谐振子。在经典允许的区域中，我们证明了对于每个经典轨迹，都有一族量子轨迹，它们都通过构成节点的某些点，并且属于经典轨迹。我们还讨论了推广到任何潜在的，并给出了一个新的定义德布罗意的波长在这样一种方式，它与相邻节点的长度分开。特别地，我们展示了当$\hbar \to 0$是经典轨道时，量子轨道是如何作为极限的。在经典的禁止区域，节点结构的轨迹丢失和粒子的速度迅速发散。
英文摘要：
In this paper, we apply the one dimensional quantum law of motion, that we recently formulated in the context of the trajectory representation of quantum mechanics, to the constant potential, the linear potential and the harmonic oscillator. In the classically allowed regions, we show that to each classical trajectory there is a family of quantum trajectories which all pass through some points constituting nodes and belonging to the classical trajectory. We also discuss the generalization to any potential and give a new definition for de Broglie's wavelength in such a way as to link it with the length separating adjacent nodes. In particular, we show how quantum trajectories have as a limit when $\hbar \to 0$ the classical ones. In the classically forbidden regions, the nodal structure of the trajectories is lost and the particle velocity rapidly diverges.
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