arXivDaily arXiv每日学术速递 周一至周五更新
arXiv quant-ph/0105033quant-ph
收藏

Aharonov-Bohm时间算符自相关函数的特征衰减

Characteristic decay of the autocorrelation functions prescribed by the Aharonov-Bohm time operator

Manabu Miyamoto

备注：
17 pages, REVTeX style file. Some relevant references are added in Sec. 2
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

本文研究了一维自由粒子系统和排斥势系统的波函数，其自相关函数的衰减比$t^{-2}$快。它然后示出，这样的波函数构成一个稠密的子集的$L^2 ({\bf R}^1)$，在几个条件下，特别是满足的平方势垒系统。这意味着自相关函数的快于$t^{-2}$ -衰减的特性对势的扰动持续存在。还可以看出，上述子集的稠密性由Aharonov-Bohm时间算子的域的稠密性保证。

英文摘要：

The wave functions, the autocorrelation functions of which decay faster than $t^{-2}$, for both the one-dimensional free particle system and the repulsive-potential system are examined. It is then shown that such wave functions constitute a dense subset of $L^2 ({\bf R}^1)$, under several conditions that are particularly satisfied by the square barrier potential system. It implies that the faster than $t^{-2}$-decay character of the autocorrelation function persists against the perturbation of potential. It is also seen that the denseness of the above subset is guaranteed by that of the domain of the Aharonov-Bohm time operator.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑