2011/08/12 by A. R. Usha Devi, H. S. Karthik
Chemistry · Computer Science · Physics and Astronomy · #Classical limit #Classical mechanics #Method of quantum characteristics #Molecular spectroscopy and chirality #Observable #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum chaos #Quantum dynamics #Quantum mechanics #Statistical physics #Theoretical physics #Uncertainty principle #quant-ph
paper · pdf · doi:10.1119/1.4720101
published as Am. J. Phys. 80, 708 (2012) · 8 pages, RevTeX, no figures
arxiv created 2011/08/12 · openalex publication_date 2012/07/17 · arxiv updated 2012/08/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.