Energy-time and frequency-time uncertainty relations: exact inequalities
Quantum Physics
2015-04-06 v1
Abstract
We give a short review of known exact inequalities that can be interpreted as "energy-time" and "frequency-time" uncertainty relations. In particular we discuss a precise form of signals minimizing the physical frequency-time uncertainty product. Also, we calculate the "stationarity time" for mixed Gaussian states of a quantum harmonic oscillator, showing explicitly that pure quantum states are "more fragile" than mixed ones with the same value of the energy dispersion. The problems of quantum evolution speed limits, time operators and measurements of energy and time are briefly discussed, too.
Cite
@article{arxiv.1504.00862,
title = {Energy-time and frequency-time uncertainty relations: exact inequalities},
author = {V. V. Dodonov and A. V. Dodonov},
journal= {arXiv preprint arXiv:1504.00862},
year = {2015}
}
Comments
39 pages, 2 figures, 300 references, to appear in the special issue of Physica Scripta "150 years of Margarita and Vladimir Man'ko"