How to generalize the Ehrenfest theorem and the uncertainty principle
Abstract
The Ehrenfest theorem and the Robertson uncertainty relation are well-known basic equations in quantum mechanics. However, there exist problematic cases, where the Ehrenfest theorem and the Robertson uncertainty relation are not correct. These cases occur when the azimuthal angle in polar or spherical coordinates is used within these equations. The purpose of this paper is to present and discuss a generalized Ehrenfest theorem and a generalized uncertainty relation which are still valid for these cases. Hereby, we define and use a mathematical operation called expectation commutator.
Keywords
Cite
@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}
}
Comments
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)