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

College Physics

Analysis of uncertain prinsiple in quantum mechanics

Liu Di-di

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

The uncertainty principle,put forward by W. K.Heisenberg in 1927,includes the uncertainty relation between two mechanical quantities and uncertainty relation between energy and time.It makes the quantum mechanics to have an integrated mathematic description and a solid physical base.In this paper,we introduce the background,the process of uncertainty principle presented,and the applied aspect of the uncertainty principle.The important role of the debate in the science developing is stressed.

Related papers

Review on entropic uncertainty relations

Lijuan Li, Fei Ming, Xue‐Ke Song +2 more

The Heisenberg uncertainty principle is one of the characteristics of quantum mechanics. With the vigorous development of quantum information theory, uncertain relations have gradually played an important role in it. In particular, in order to solved the shortcomings of the concept in the initial formulation of the uncertainty principle, we brought entropy into the uncertainty relation, after that, the entropic uncertainty relation has exploited the advantages to the full in various applications. As we all know the entropic uncertainty relation has became the core element of the security analysis of almost all quantum cryptographic protocols. This review mainly introduces development history and latest progress of uncertain relations. After Heisenberg's argument that incompatible measurement results are impossible to predict, many scholars, inspired by this viewpoint, have made further relevant investigations. They combined the quantum correlation between the observable object and its environment, and carried out various generalizations of the uncertainty relation to obtain more general formulas. In addition, it also focuses on the entropy uncertainty relationship and quantum-memory-assisted entropic uncertainty relation, and the dynamic characteristics of uncertainty in some physical systems. Finally, various applications of the entropy uncertainty relationship in the field of quantum information are discussed, from randomnesss to wave-particle duality to quantum key distribution.

Acta Physica Sinica•Jan 1, 2022•9 citations

A brief analysis of the physical significance of Heisenberg's uncertainty principle

Guannan Zhou

The principle of uncertainty is one of the essential principles of quantum mechanics as it outlines that there is a reflective limit to the measurement of microscopic particle motion. However it is impossible to measure at once and accurately both the position and momentum data of any microscopic particle no matter what means are used to do so. This paper starts by discussing the notion and mathematical derivation of the uncertainty principle as put forth by Heisenberg explaining the physical relevance of the principle. It introduces the natural uncertainty the principle introduces to the dynamics of particles in the microscopic world, and the significant part it plays in the theory of quantum mechanics. The article overviews the explanations of the principle on phenomena including atomic stability and scanning tunneling microscopes, and the interference of measurement actions on the states of particles and the shortcomings of measurement precision. According to the wave-particle duality of quantum mechanics, this article gives a required theoretical basis of microscopic phenomena. Likewise, the use of the research theory on the uncertainty principle by distinguished scholars in the physics fraternity helps the readers in achieving the knowledge in related subjects more easily.

Advances in Engineering Innovation•Apr 7, 2026•0 citations

Why does uncertainty come in quantum mechanics?

Muhammad Yasin

In 1927 Heisenberg has invented the uncertainty principle. The principle of uncertainty is, "It is impossible to determine the position and momentum of a particle at the same time."The more accurately the momentum is measured, the more uncertain the position will be. Just knowing the position would make the momentum uncertain. Einstein was adamant against this principle until his death. He thought that particles have some secret rules. Einstein thought, "The uncertainty principle is incomplete. There is a mistake somewhere that has resulted in uncertainty. Many did not accept Einstein then. But I'm sure Einstein was right then, there are secret rules for particles. Heisenberg's uncertainty principle is also 100% correct . I recently published a research paper named "Quantum Certainty Mechanics"[1], which shows the principle of measuring the momentum and position of particles by the quantum certainty principle. Why uncertainty comes from certainty is the main topic of this research paper. When the value of the energy absorbed by the electron in the laboratory is calculated, the uncertainty is removed. The details are discussed below.

•Mar 2, 2021•0 citations

Mathematics Behind the Heisenberg Uncertainty Principle

Dewi Wulandari

Most physics books do not reveal clearly how the Heisenberg uncertainty principle was derived. This uncertainty comes from the consequence of the wave-particle duality of matter giving statement that position and momentum cannot be measured in the same time. This article tries to reveal mathematics background behind the expression the Heisenberg uncertainty using supported mathematics background such as Fourier transform, Fourier transform integral, the probability of Gaussian distribution and it ends up with the expression of wave function which describe the localized particle giving relation Heisenberg uncertainty principle.

Jurnal Penelitian Pendidikan IPA•Apr 30, 2023•0 citations

The falsification of the non-statistical interpretation of the uncertainty principle and the breakthrough of the statistical interpretation -- From the Uncertainty Principle to the Deterministic Rule

De-Long Duan

It is well known that the problem of divergence in the physical interpretation of quantum mechanics originating from the uncertainty principle has not yet been resolved. Attempting to clear the constraints and confusion of this situation for the further development of quantum technology, this article traces the original derivation and the physical meaning of the Heisenberg uncertainty principle, analyzes the Einstein photon-box thought-experiment, and studies the limits of the relationships under different action scenarios. By analyzing the statistical distribution of quantum mechanical quantities, the result of the destruction of the non-statistical interpretation uncertainty relation in the electromagnetic interaction scenarios is obtained; through analyzing of the photon box thought experiment, the logical contradiction of Bohr's argument was discovered; by examining the set of interaction scenarios, a description method for determining the mechanical state of microscopic particles was put forward; according to the analysis of the hydrogen atom transition radiation process, basing on the principle of conservation of energy, the result of the lower limit of the uncertainty relation in the gravitational scene is much smaller than that in the existing electromagnetic scene is obtained, which mean the lower limit of uncertainty principle is broken. The research in this article has received an affirmative answer to Einstein's God does not play dice with the Universe. The research of this article is helpful to enhance the understanding of quantum physical phenomena in the microscopic world, and we hope it could render some theoretical support to investigating the physical basis of quantum technology.

arXiv:2103.03513•Mar 5, 2021•0 citations

Schrödinger equation for various quantum systems based on Heisenberg's uncertainty principle

Kexin An

This article establishes the proof of the Schrödinger equation for numerous quantum systems, utilizing Heisenberg's uncertainty principle. The Fourier transform connects functions in the time and frequency domains, resulting in the mathematical inequality that is the foundation of the uncertainty principle. In the part of Methods and Theory, the article derives the uncertainty principle through Fourier transforms by defining the mean and variance of angular frequency and time, and subsequently expanding the integral. This establishes the fundamental connection between time and frequency domains, illustrating the constraints imposed by quantum mechanics. In the part of Results and Application, the article applies the uncertainty principle to derive the Schrödinger equation under different conditions: free particle, particle in a box, harmonic oscillator, and hydrogen atom. For each case, the article assumes wave function solutions, uses the uncertainty in position and momentum to estimate kinetic and potential energies, and shows that the total energy matches the ground state energy derived from the Schrödinger equation. The results highlight the critical role of Heisenberg's uncertainty principle in understanding key aspects of quantum mechanics, providing a unified framework for these diverse systems.

Theoretical and Natural Science•Sep 27, 2024•0 citations
The uncertainty principle,put forward by W. K.Heisenberg in 1927,includes the uncertainty relation between two mechanical quantities and uncertainty relation between energy and time.It makes the quantum mechanics to have an integrated mathematic description and a solid physical base.In this paper,we introduce the background,the process of uncertainty principle presented,and the applied aspect of the uncertainty principle.The important role of the debate in the science developing is stressed.
The Heisenberg uncertainty principle is one of the characteristics of quantum mechanics. With the vigorous development of quantum information theory, uncertain relations have gradually played an important role in it. In particular, in order to solved the shortcomings of the concept in the initial formulation of the uncertainty principle, we brought entropy into the uncertainty relation, after that, the entropic uncertainty relation has exploited the advantages to the full in various applications. As we all know the entropic uncertainty relation has became the core element of the security analysis of almost all quantum cryptographic protocols. This review mainly introduces development history and latest progress of uncertain relations. After Heisenberg's argument that incompatible measurement results are impossible to predict, many scholars, inspired by this viewpoint, have made further relevant investigations. They combined the quantum correlation between the observable object and its environment, and carried out various generalizations of the uncertainty relation to obtain more general formulas. In addition, it also focuses on the entropy uncertainty relationship and quantum-memory-assisted entropic uncertainty relation, and the dynamic characteristics of uncertainty in some physical systems. Finally, various applications of the entropy uncertainty relationship in the field of quantum information are discussed, from randomnesss to wave-particle duality to quantum key distribution.
The principle of uncertainty is one of the essential principles of quantum mechanics as it outlines that there is a reflective limit to the measurement of microscopic particle motion. However it is impossible to measure at once and accurately both the position and momentum data of any microscopic particle no matter what means are used to do so. This paper starts by discussing the notion and mathematical derivation of the uncertainty principle as put forth by Heisenberg explaining the physical relevance of the principle. It introduces the natural uncertainty the principle introduces to the dynamics of particles in the microscopic world, and the significant part it plays in the theory of quantum mechanics. The article overviews the explanations of the principle on phenomena including atomic stability and scanning tunneling microscopes, and the interference of measurement actions on the states of particles and the shortcomings of measurement precision. According to the wave-particle duality of quantum mechanics, this article gives a required theoretical basis of microscopic phenomena. Likewise, the use of the research theory on the uncertainty principle by distinguished scholars in the physics fraternity helps the readers in achieving the knowledge in related subjects more easily.
In 1927 Heisenberg has invented the uncertainty principle. The principle of uncertainty is, "It is impossible to determine the position and momentum of a particle at the same time."The more accurately the momentum is measured, the more uncertain the position will be. Just knowing the position would make the momentum uncertain. Einstein was adamant against this principle until his death. He thought that particles have some secret rules. Einstein thought, "The uncertainty principle is incomplete. There is a mistake somewhere that has resulted in uncertainty. Many did not accept Einstein then. But I'm sure Einstein was right then, there are secret rules for particles. Heisenberg's uncertainty principle is also 100% correct . I recently published a research paper named "Quantum Certainty Mechanics"[1], which shows the principle of measuring the momentum and position of particles by the quantum certainty principle. Why uncertainty comes from certainty is the main topic of this research paper. When the value of the energy absorbed by the electron in the laboratory is calculated, the uncertainty is removed. The details are discussed below.
Most physics books do not reveal clearly how the Heisenberg uncertainty principle was derived. This uncertainty comes from the consequence of the wave-particle duality of matter giving statement that position and momentum cannot be measured in the same time. This article tries to reveal mathematics background behind the expression the Heisenberg uncertainty using supported mathematics background such as Fourier transform, Fourier transform integral, the probability of Gaussian distribution and it ends up with the expression of wave function which describe the localized particle giving relation Heisenberg uncertainty principle.
It is well known that the problem of divergence in the physical interpretation of quantum mechanics originating from the uncertainty principle has not yet been resolved. Attempting to clear the constraints and confusion of this situation for the further development of quantum technology, this article traces the original derivation and the physical meaning of the Heisenberg uncertainty principle, analyzes the Einstein photon-box thought-experiment, and studies the limits of the relationships under different action scenarios. By analyzing the statistical distribution of quantum mechanical quantities, the result of the destruction of the non-statistical interpretation uncertainty relation in the electromagnetic interaction scenarios is obtained; through analyzing of the photon box thought experiment, the logical contradiction of Bohr's argument was discovered; by examining the set of interaction scenarios, a description method for determining the mechanical state of microscopic particles was put forward; according to the analysis of the hydrogen atom transition radiation process, basing on the principle of conservation of energy, the result of the lower limit of the uncertainty relation in the gravitational scene is much smaller than that in the existing electromagnetic scene is obtained, which mean the lower limit of uncertainty principle is broken. The research in this article has received an affirmative answer to Einstein's God does not play dice with the Universe. The research of this article is helpful to enhance the understanding of quantum physical phenomena in the microscopic world, and we hope it could render some theoretical support to investigating the physical basis of quantum technology.
This article establishes the proof of the Schrödinger equation for numerous quantum systems, utilizing Heisenberg's uncertainty principle. The Fourier transform connects functions in the time and frequency domains, resulting in the mathematical inequality that is the foundation of the uncertainty principle. In the part of Methods and Theory, the article derives the uncertainty principle through Fourier transforms by defining the mean and variance of angular frequency and time, and subsequently expanding the integral. This establishes the fundamental connection between time and frequency domains, illustrating the constraints imposed by quantum mechanics. In the part of Results and Application, the article applies the uncertainty principle to derive the Schrödinger equation under different conditions: free particle, particle in a box, harmonic oscillator, and hydrogen atom. For each case, the article assumes wave function solutions, uses the uncertainty in position and momentum to estimate kinetic and potential energies, and shows that the total energy matches the ground state energy derived from the Schrödinger equation. The results highlight the critical role of Heisenberg's uncertainty principle in understanding key aspects of quantum mechanics, providing a unified framework for these diverse systems.