Title:	The uncertainity product of position and momentum in classical dynamics
Authors:	Usha Devi, A.R. Karthik, H.S.
Issue Date:	Aug-2012
Publisher:	American Association of Physics Teachers
Citation:	American Journal of Physics, 2012, Vol. 80, p708
Abstract:	It is generally believed that the classical regime emerges as a limiting case of quantum theory. Exploring such quantum-classical correspondences provides a deeper understanding of foundational aspects and has attracted a great deal of attention since the early days of quantum theory. It has been proposed that since a quantum mechanical wave function describes an intrinsic statistical behavior, its classical limit must correspond to a classical ensemble—not to an individual particle. This idea leads us to ask how the uncertainty product of canonical observables in the quantum realm compares with the corresponding dispersions in the classical realm. In this paper, we explore parallels between the uncertainty product of position and momentum in stationary states of quantum systems and the corresponding fluctuations of these observables in the associated classical ensemble. We confine ourselves to one-dimensional conservative systems and show, with the help of suitably defined dimensionless physical quantities, that first and second moments of the canonical observables match with each other in the classical and quantum descriptions—resulting in identical structures for the uncertainty relations in both realms.
Description:	Open Access
URI:	http://hdl.handle.net/2289/7888
ISSN:	0002-9505
Alternative Location:	https://doi.org/10.1119/1.4720101
Copyright:	2012 American Association of Physics Teachers
Appears in Collections:	Research Papers (LAMP)

Items in RRI Digital Repository are protected by copyright, with all rights reserved, unless otherwise indicated.