Universality in Uncertainty Relations for a Quantum Particle
Abstract
A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is bounded from below. Whenever a global minimum exists, an uncertainty relation has been obtained. The squeezed number states of a harmonic oscillator are found to be universal: no other pure or mixed states will saturate any such relation. Geometrically, we identify a convex uncertainty region in the space of second moments which is bounded by the inequality derived by Robertson and Schr\"{o}dinger. Our approach not only unifies existing uncertainty relations but also leads to new inequalities for second moments.
Cite
@article{arxiv.1509.02146,
title = {Universality in Uncertainty Relations for a Quantum Particle},
author = {Spiros Kechrimparis and Stefan Weigert},
journal= {arXiv preprint arXiv:1509.02146},
year = {2016}
}
Comments
22 pages, 4 figures. Material rearranged to match published version