用于描述谐振子及其他一维问题本征态的路径分布
量子物理
2025-11-18 v6
摘要
本文描述了路径的概率幅如何求和形成谐振子以及其他简单一维问题的波函数。利用各问题已知的闭式基于路径的传播子，写出描述波函数的积分表达式。该表达式通常取为对粒子初始位置的积分，但此处将其重新表述为关于与路径两端点间运动相关的特征动量。以此方式，所得表达式可利用平稳相分析的推广进行分析，从而得到精确描述各本征态的路径分布。这些分布对所有传播时间均有效，但当在长时间下求值时，它们变为特征动量的实值非负函数。特别地，对谐振子发现一个略宽的分布，其峰值动量对应的经典能量恰等于所描述态的能量本征值。
引用
@article{arxiv.2306.11155,
title = {Path distributions for describing eigenstates of the harmonic oscillator and other 1-dimensional problems},
author = {Randall M. Feenstra},
journal= {arXiv preprint arXiv:2306.11155},
year = {2025}
}
备注
26 page, 10 figures; in v2, added refs. 43 and 44 along with a brief description of the latter, and made a few minor typographical corrections; in v3, added several explanatory sentences following Eqs. (12) and (16) and made a few additional minor corrections; further minor correction in v4; computer code added in v5; minor change in notation in v6