如何推广埃伦费斯特定理与不确定性原理
量子物理
2019-09-24 v3
摘要
埃伦费斯特定理与 Robertson 不确定性关系是量子力学中众所周知的基本方程。然而，存在一些有问题的情形，其中埃伦费斯特定理与 Robertson 不确定性关系并不成立。这些情形出现在极坐标或球坐标中的方位角被用于这些方程时。本文的目的是提出并讨论一个广义的埃伦费斯特定理与一个广义的不确定性关系，它们在上述情形中仍然有效。为此，我们定义并使用了一种称为期望对易子的数学运算。
引用
@article{arxiv.1904.06177,
title = {How to generalize the Ehrenfest theorem and the uncertainty principle},
author = {Klaus Renziehausen and Ingo Barth},
journal= {arXiv preprint arXiv:1904.06177},
year = {2019}
}
备注
7 pages. We withdrew this work because the self-adjointness of two operators A and B is defined in a manner that the expectation commutator A#B defined in Eq. (4) is always zero. Thus, the generalized Ehrenfest theorem Eq. (6) is just equal to the Ehrenfest theorem Eq. (7), and the generalized uncertainty relation Eq. (12) is just equal to the Robertson uncertainty relation Eq. (13)