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

Position-momentum uncertainty relation for a particle in the one-dimensional infinite potential well:revisited after calculation

Jia Liu

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

Position and momentum uncertainties,Δx and △p,for a particle in the one-dimensional infinite potential well are calculated. It shows that they obey the general uncertainty relation △x·△p■/2 though,yet they follow the same trend in changing among different states. Similar phenomenon for △t and △E (where △ has a distinct definition) also has been confirmed in some spectral measurements.

Related papers

Entropic uncertainty relations for the infinite well

Vladimír Majerník, Lukáš Richterek

We calculate the entropic and standard uncertainty relations for the position and momentum of the infinite potential well as functions of its quantum states. We show that the entropic uncertainty relations express more adequately the uncertainty principle than the standard ones which use the dispersions as measures of the uncertainties for two non-commuting observables.

Journal of Physics A Mathematical and General•Feb 21, 1997•53 citations

Uncertainty relations for a particle confined in a finite square well potential

Akira Tamura, Yohhei Tatsumi

Abstract In order to specify the uncertainty relation for a particle confined in a finite square well potential we derived the standard deviation of momentum Δ p and that of position Δ x . It is shown that Δ p has a peak as a function of the well width and both Δ x and Δ p ⋅ Δ x have a dip in contrast to the case of the particle confined in an infinite square well potential. We clarified that Δ p 0 ⋅ Δ x 0 of the particle occupying the ground state exists in the finite range as a function of the well width and the potential-barrier height, but a particle confined in an infinite square well potential has a constant Δ p 0 ⋅ Δ x 0 . In addition, we found that the values of Δ p n ⋅ Δ x n for excited states diverge in a certain range of well widths, where the energy level of the confined particle exceeds the potential barrier.

European Journal of Physics•Aug 4, 2017•4 citations

Simple Deduction and Correct Understanding of Uncertainty Relation

Weijun Yu

According to de Broglie wave hypothesis,based on one dimensional infinite wall and by using standing wave condition,distribution of momentum of a particle in one dimensional infinite wall is deduced.With reference to the definition of uncertainty,position uncertainty and momentum uncertainty are calculated and uncertainty relation of one dimensional infinite wall is deduced.Correct understanding uncertainty relation is discussed.

Journal of Yancheng Institute of Technology•Jan 1, 2006•0 citations

The Uncertainty Relation of Linear Oscillator

Jian-Jun Liu

Using the uncertainty principle of quantum mechanics,in the system of one-dimensional linear oscillator,position and momentum uncertainties and kinetic energy and potential energy uncertainties are calculated quantitatively.It is shown that they obey the general uncertainty relations.Some misunderstanding and misdescription about the uncertain relations are explained.

Journal of Hebei Normal University•Jan 1, 2012•0 citations

Heisenberg uncertainty relation and statistical measures in the square well

Ricardo López‐Ruiz, Jaime Sañudo A

A non stationary state in the one-dimensional infinite square well formed by a combination of the ground state and the first excited one is considered. The statistical complexity and the Fisher-Shannon entropy in position and momentum are calculated with time for this system. These measures are compared with the Heisenberg uncertainty relation, ΔxΔp. It is observed that the extreme values of ΔxΔp coincide in time with extreme values of the other two statistical magnitudes.

arXiv:1108.2376•Communications in Numerical Analysis•Jan 1, 2012•1 citation

The Momentum Probability Amplitude and the Equality Form Uncertain Relation of One-dimensional Harmonic Oscillator

Luo Ling-xiao

In this paper,the uncertainty in positon,the momentum probability amplitude and momentum probability density's recurrence formulas,the uncertainty in momentum and the uncertain relation of the equality form momentum-position of one-dimensional harmonic oscillator were deduced.This paper also pointed out that the lower limit of one-dimensional harmonic oscillator's ΔpΔx is exactly the lower limit of /2 which given by the general form of the uncertain relation,however the lower limit of one-dimensional infinite well's ΔpΔx is a little bigger than /2,so the lower limit of a quantum system's ΔpΔx is needn't equal to /2.

Journal of Xuchang University•Jan 1, 2004•0 citations
Position and momentum uncertainties,Δx and △p,for a particle in the one-dimensional infinite potential well are calculated. It shows that they obey the general uncertainty relation △x·△p■/2 though,yet they follow the same trend in changing among different states. Similar phenomenon for △t and △E (where △ has a distinct definition) also has been confirmed in some spectral measurements.
Abstract In order to specify the uncertainty relation for a particle confined in a finite square well potential we derived the standard deviation of momentum Δ p and that of position Δ x . It is shown that Δ p has a peak as a function of the well width and both Δ x and Δ p ⋅ Δ x have a dip in contrast to the case of the particle confined in an infinite square well potential. We clarified that Δ p 0 ⋅ Δ x 0 of the particle occupying the ground state exists in the finite range as a function of the well width and the potential-barrier height, but a particle confined in an infinite square well potential has a constant Δ p 0 ⋅ Δ x 0 . In addition, we found that the values of Δ p n ⋅ Δ x n for excited states diverge in a certain range of well widths, where the energy level of the confined particle exceeds the potential barrier.
In this paper,the uncertainty in positon,the momentum probability amplitude and momentum probability density's recurrence formulas,the uncertainty in momentum and the uncertain relation of the equality form momentum-position of one-dimensional harmonic oscillator were deduced.This paper also pointed out that the lower limit of one-dimensional harmonic oscillator's ΔpΔx is exactly the lower limit of /2 which given by the general form of the uncertain relation,however the lower limit of one-dimensional infinite well's ΔpΔx is a little bigger than /2,so the lower limit of a quantum system's ΔpΔx is needn't equal to /2.