Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Southwest University

Fourier transform and uncertainty principle

Liu Yuan-she

Published Jan 1, 2003• 1 citation
OpenAlex

Abstract

Starting from the definition of Fourier transform, uncertainty principle in quantum mechanics is educed by the short term Fourier transform for the time variable signal. And the necessity of the relation between them is explained in this article.

Related papers

The Maths Explained of Heisenberg's Uncertainty Principle in the Quantum Mechanics and its Application in the Wavelet Analysis

Deng Feng-ru

Starting from the definition of Fourier transform,uncertainty principle in quantum mechanics is educed by the short term Fourier transform for the time variable signal.And the necessity of the relation between them is explained in this article,and an Ap- plication example about uncertainty principle in the wavelet analysis is given.

Journal of North China Institute of Aerospace Engineering•Jan 1, 2006•0 citations

Single-Slit Diffraction and the Uncertainty Principle

Frank Rioux

This short article emphasizes that a consideration of diffraction phenomena is an excellent way to illustrate the uncertainty principle. Or, it could also be claimed that diffraction has a simple quantum mechanical interpretation based on the uncertainty principle and the Fourier transform between position and momentum space.

Journal of Chemical Education•Aug 1, 2005•6 citations

The Uncertainty Principle with Fourier Transform Derivatives

Feifei Qu

Abstract The classical uncertainty principle works for smooth signal functions. In our work, we apply the Fourier transform derivatives for the study of uncertainty principle, so that the smoothness condition for the signal functions is not required. At first, the amplitude and phase derivatives of vector-valued signal functions based on the Fourier transform are defined. Then we obtain a strong form of the uncertainty principle.

Journal of Physics Conference Series•Jul 1, 2023•0 citations

Role of Fourier transform in quantum mechanics: Applications and implications

Yuhuan Lyu

The Fourier transform, as a fundamental mathematical tool, plays a pivotal role in quantum mechanics. Its significance extends to wave function analysis, solving the Schrödinger equation, and elucidating the relationship between position and momentum. In this review article, the primary objective is to summarize the diverse applications of the Fourier transform in quantum mechanics. This paper will delve into key applications, highlighting the uncertainty principle, the Planck-Einstein relation, and the Fourier transform solution of the Schrödinger equation. These theorems and relationships not only facilitate the mathematical manipulation of quantum states but also lay the theoretical foundation of quantum mechanics. By exploring these critical aspects, the author aims to provide a comprehensive understanding of how the Fourier transform underpins the core principles of quantum theory, offering valuable insights into the wave particle duality and the probabilistic nature of quantum systems. This discussion will emphasize the essential nature of the Fourier transform in both theoretical development and practical problem-solving within quantum mechanics

Theoretical and Natural Science•Sep 20, 2024•0 citations

Nazarov’s uncertainty principle for fractional Fourier transform

Sri Sulasteri, Mawardi Bahri, Nasrullah Bachtiar +2 more

In the present work, we provide the definition of the fractional Fourier transform and then investigate its properties. Based on the properties, we derive the Nazarov’s uncertainty principle for the fractional Fourier transform.

AIP conference proceedings•Jan 1, 2024•0 citations

The Uncertainty Principle for the Short-Time Fourier Transform and Wavelet Transform

Leon W. Cohen

We obtain both a global and local uncertainty principle for the short-time Fourier transform. Explicit expressions are obtained for the uncertainty product in terms of the uncertainty product of the signal and window. Although the uncertainty product of the spectrogram is not the sum of the uncertainty products of the window and signal, nonetheless, we show that the global uncertainty product has to be greater than one. We also derive local uncertainty relations which indicate how the local spread in time and frequency are related at a particlar time–frequency point. In addition, we obtain general results for the time, scale, and frequency moments of the scalogram in terms of the moments of the signal and mother wavelet. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Birkhäuser Boston eBooks•Jan 1, 2001•29 citations
The Fourier transform, as a fundamental mathematical tool, plays a pivotal role in quantum mechanics. Its significance extends to wave function analysis, solving the Schrödinger equation, and elucidating the relationship between position and momentum. In this review article, the primary objective is to summarize the diverse applications of the Fourier transform in quantum mechanics. This paper will delve into key applications, highlighting the uncertainty principle, the Planck-Einstein relation, and the Fourier transform solution of the Schrödinger equation. These theorems and relationships not only facilitate the mathematical manipulation of quantum states but also lay the theoretical foundation of quantum mechanics. By exploring these critical aspects, the author aims to provide a comprehensive understanding of how the Fourier transform underpins the core principles of quantum theory, offering valuable insights into the wave particle duality and the probabilistic nature of quantum systems. This discussion will emphasize the essential nature of the Fourier transform in both theoretical development and practical problem-solving within quantum mechanics
We obtain both a global and local uncertainty principle for the short-time Fourier transform. Explicit expressions are obtained for the uncertainty product in terms of the uncertainty product of the signal and window. Although the uncertainty product of the spectrogram is not the sum of the uncertainty products of the window and signal, nonetheless, we show that the global uncertainty product has to be greater than one. We also derive local uncertainty relations which indicate how the local spread in time and frequency are related at a particlar time–frequency point. In addition, we obtain general results for the time, scale, and frequency moments of the scalogram in terms of the moments of the signal and mother wavelet. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.