Physical Review Letters

Position-Momentum Uncertainty Relations in Stochastic Mechanics

Diego de Falco, S. De Martino, Silvio De Siena

Published Jul 19, 1982• 41 citations

Abstract

A simple inequality relating the root mean square deviations of position and osmotic velocity for a diffusion process is presented and, in the framework of Nelson's stochastic mechanics, is related to the Heisenberg position-momentum uncertainty relations.

DOI: 10.1103/physrevlett.49.181

Related papers

Uncertainty relations in stochastic mechanics

Simon Golin

Position–momentum uncertainty in Nelson’s stochastic mechanics [Phys. Rev. 150, 1079 (1966)] has previously been investigated by de la Peña-Auerbach and Cetto [Phys. Lett. A 39, 65 (1972)]. In this paper their result is generalized, and full equivalence between the uncertainty relations in stochastic mechanics and conventional quantum mechanics is established. Force–momentum uncertainty is also considered.

Journal of Mathematical PhysicsNov 1, 198523 citations

Position-Momentum Uncertainty Relations in Stochastic Mechanics.

Diego de Falco, Salvatore De Martino, Silvio De Siena

We have only recently become amare of an article by

Physical Review LettersFeb 28, 19834 citations

Minimum uncertainty and squeezing in diffusion processes and stochastic quantization

Salvatore DeMartino, Silvio DeSiena, Fabrizo Illuminati +1 more

We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states. 1

May 1, 19940 citations

Minimum Uncertainty, Coherence and Squeezing in Diffusion Processes, and Stochastic Quantization

S. De Martino, Silvio De Siena, Fabrizio Illuminati +1 more

arXiv:hep-th/9310109Oct 18, 19931 citation

Semiclassical Double-Inequality on Heisenberg Uncertainty Relation in 1D

Klaus Bering

We prove a double-inequality for the product of uncertainties for position and momentum of bound states for 1D quantum mechanical systems in the semiclassical limit.

arXiv:1405.6478Acta Physica Polonica AJun 1, 20160 citations

More certainty about the uncertainty principle

Jan Hilgevoord, Jos Uffink

The uncertainty principle of position and momentum is a mathematically more involved relation than is usually realised. The well-known Heisenberg uncertainty relation between standard deviations is much too weak to express the uncertainty principle. By employing other notions of width, relations are given which do express the uncertainty principle.

European Journal of PhysicsJul 1, 198521 citations