波包自由传播中的轨迹和经典运动的感知

John S. Briggs
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引用次数: 3

摘要

可归一化波包在时间中的自由传播是连续统量子力学中最古老的问题。它从微观到宏观距离的运动是大多数量子系统在实验中被检测到的方式。尽管自1927年以来,人们对这个问题进行了大量的研究和分析,并在许多教科书中提出,但这里从半经典力学的角度对这个问题进行了重新评价。特别的方面是粒子从原子维度的区域发出的确定性轨迹的出现,以及波函数作为描述单个粒子或相同粒子的集合的解释。在可能的波包中,由于在实空间和动量空间中随时间解的简单精确形式,高斯形式的波包被研究得最多。此外,这种形式在激光光学中也很重要。在这里等价的时间依赖Schrödinger方程的准轴方程的传播光被明确地证明。这种平行有助于理解轨迹概念的相关性以及将量子运动视为经典所必需的条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Trajectories and the perception of classical motion in the free propagation of wave packets

Trajectories and the perception of classical motion in the free propagation of wave packets
The free propagation in time of a normalisable wave packet is the oldest problem of continuum quantum mechanics. Its motion from microscopic to macroscopic distance is the way in which most quantum systems are detected experimentally. Although much studied and analysed since 1927 and presented in many textbooks, here the problem is re-appraised from the standpoint of semi-classical mechanics. Particular aspects are the emergence of deterministic trajectories of particles emanating from a region of atomic dimension and the interpretation of the wave function as describing a single particle or an ensemble of identical particles. Of possible wave packets, that of Gaussian form is most studied due to the simple exact form of the time-dependent solution in real and in momentum space. Furthermore, this form is important in laser optics. Here the equivalence of the time-dependent Schrödinger equation to the paraxial equation for the propagation of light is demonstrated explicitly. This parallel helps to understand the relevance of trajectory concepts and the conditions necessary for the perception of quantum motion as classical.
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