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We obtain a new version of the Uncertainty Principle for functions with Fourier transforms supported on a lacunary set of intervals. This is a generalization of Zygmund's theorem on lacunary trigonometric series to the real line in the…

Classical Analysis and ODEs · Mathematics 2007-05-23 O. Kovrizhkin

Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…

Quantum Physics · Physics 2021-05-05 Yunlong Xiao , Kuntal Sengupta , Siren Yang , Gilad Gour

The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We…

Quantum Physics · Physics 2015-09-22 Jun Zhang , Yang Zhang , Chang-shui Yu

In this paper we uses an I.I. Hirschman-W. Beckner entropy argument to give an uncertainty inequality for the $q$-Bessel Fourier transform: $$ \mathcal{F}_{q,v}f(x)=c_{q,v}\int_{0}^{\infty}f(t)j_{v}(xt,q^{2})t^{2v +1}d_{q}t, $$ where…

Classical Analysis and ODEs · Mathematics 2008-07-01 Lazhar Dhaouadi

In this paper the uncertainty principle is found via characteristics of continuous and nowhere differentiable functions. We prove that any physical system that has a continuous and nowhere differentiable position function is subject to an…

General Physics · Physics 2021-07-13 Faycal Ben Adda , Helene Porchon

A sharper uncertainty inequality which exhibits a lower bound larger than that in the classical N-dimensional Heisenberg's uncertainty principle is obtained, and extended from N-dimensional Fourier transform domain to two N-dimensional…

Mathematical Physics · Physics 2019-06-14 Zhichao Zhang

The uncertainty principle, originally formulated by Heisenberg, dramatically illustrates the difference between classical and quantum mechanics. The principle bounds the uncertainties about the outcomes of two incompatible measurements,…

Quantum Physics · Physics 2011-03-02 Mario Berta , Matthias Christandl , Roger Colbeck , Joseph M. Renes , Renato Renner

The full algebra of relativistic quantum mechanics (Lorentz plus Heisenberg) is unstable. Stabilization by deformation leads to a new deformation parameter $\epsilon \ell ^{2}$, $\ell $ being a length and $\epsilon$ a $\pm$ sign. The…

Quantum Physics · Physics 2009-11-07 Eric Carlen , R. Vilela Mendes

We prove a new uncertainty principle for square-integrable irreducible unitary representations of connected Lie groups. The concentration of the matrix coefficients is measured in terms of weighted $L^p$ norms, with weights in the local…

Classical Analysis and ODEs · Mathematics 2024-03-05 Fabio Nicola

A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given…

Quantum Physics · Physics 2022-04-27 Jaeha Lee

In this paper we critically analyse W. Heisenberg's arguments against the ontology of point particles following trajectories in quantum theory, presented in his famous 1927 paper and in his Chicago lectures (1929). Along the way, we will…

History and Philosophy of Physics · Physics 2022-12-14 Serj Aristarhov

The aim of this paper is two prove two versions of the Dynamical Uncertainty Principlefor the Schr\"odinger equation $i\partial_s u=\mathcal{L}u+Vu$, $u(s=0)=u_0$ where$\mathcal{L}$ is the sub-Laplacian on the Heisenberg group.We show two…

Classical Analysis and ODEs · Mathematics 2025-02-21 Philippe Jaming , Somnath Gosh

In two articles, the authors claim that the Heisenberg uncertainty principle limits the precision of simultaneous measurements of the position and velocity of a particle and refer to experimental evidence that supports their claim. It is…

General Physics · Physics 2007-07-12 Elias P. Gyftopoulos

The aim of this paper is establish the Heisenberg-Pauli-Weyl uncertainty principle and Donho-Stark's uncertainty principle for the Weinstein $L^2$-multiplier operators.

Classical Analysis and ODEs · Mathematics 2020-02-24 Ahmed Saoudi

As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…

Quantum Physics · Physics 2019-09-18 Jie Xie , Songtao Huang , Li Zhou , Aonan Zhang , Huichao Xu , Man-Hong Yung , Nengkun Yu , Lijian Zhang

Heisenberg's uncertainty relation is commonly regarded as defining a level of unpredictability that is fundamentally incompatible with the deterministic laws embodied in classical field theories such as Einstein's general relativity. We…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Paul S. Wesson

In this paper we review the Heisenberg uncertainty principle in a discrete setting and, as in the classical uncertainty principle, we give it a dynamical sense related to the discrete Schr\"odinger equation. We study the convergence of the…

Analysis of PDEs · Mathematics 2014-11-04 Aingeru Fernández-Bertolin

The uncertainty principle generally prohibits determination of certain pairs of quantum mechanical observables with arbitrary precision and forms the basis of indeterminacy in quantum mechanics. It was Heisenberg who used the famous…

The entropic uncertainty principle as outlined by Maassen and Uffink for a pair of non-degenerate observables in a finite level qusystem is generalized here to the case of a pair of arbitrary quantum measurements. In particular, our result…

Quantum Physics · Physics 2007-05-23 M Krishna , K R Parthasarathy

In this article we consider linear operators satisfying a generalized commutation relation of a type of the Heisenberg-Lie algebra. It is proven that a generalized inequality of the Hardy's uncertainty principle lemma follows. Its…

Functional Analysis · Mathematics 2015-05-19 Toshimitsu Takaesu