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 Shanghai University (English Edition)

A Study on Reflection Phase Time of Particles Passing through a Potential Well

Chun-Fang Li

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

To understand the physical meaning of phase time further more, we discuss the reflection phase time of quantum-particles passing though a potential well It is shown that the reflection phase time is equal to the transmission phase time in value and negative under certain conditions for a square potential well by analyzing While quantum-particles passing through the potential well, we think that this course can be described only with the velocity of energy of quantum mechanics whether or not they are reflected or transmitted eventually

Related papers

A Study on Negative Phase for Particles Passing Through a Potential Well

Xu Gang

This article studies phase time for particles passing through a potential well and finds that the phase time of particles passing through a potential well is the periodical resonance transmission and always negative when the energy of incident particles and the thickness of potential well satisfy certain conditions.

Journal of Chongqing Three-gorges University•Jan 1, 2008•0 citations

Tunneling times

Partha Ghose

Introduction In classical physics it is meaningful to ask the question, ‘How much time does a particle take to pass through a given region?’ The interesting question in quantum mechanics is: does a particle take a definite time to tunnel through a classically forbidden region? The question has been debated ever since the idea that there was such a time in quantum theory was first put forward by MacColl way back in 1932 [253]. A plethora of times has since then been proposed, and the answer seems to depend on the interpretation of quantum mechanics one uses. A reliable answer is clearly of great importance for the design of high-frequency quantum devices, tunnelling phenomena (as, for example, in scanning tunneling microscopy), nuclear and chemical reactions and, of course, for purely conceptual reasons. Most of the controversies centre around simple and intuitive notions in idealized one-dimensional models in a scattering configuration in which a particle (usually represented by a wave packet) is incident on a potential barrier localized in the interval [ a, b ]. Three kinds of time have been defined in this context. One, called the transmission time τ T ( a, b ), is the average time spent within the barrier region by the particles that are eventually transmitted. Similarly, the reflection time τ R ( a, b ) is the average time spent within the barrier region by the particles that are eventually reflected.

Cambridge University Press eBooks•Apr 29, 1999•0 citations

The Velocities of Energy and Traversing Times of Particles Passing Through A Potential Well and Photons TravellingThrough A Thin Glass Plate

Yuwu Zhang

A physically meaningful speed-the velocity of energy is used, which is similar to the energy speed in electromagnetism, to describe the process of particles passing through a potential well. It is shown that the corresponding traversing time of particles isn't negative as the phase time, which is negative under certain conditions. This speed can also describe the process of photons travelling through a non-dispersing thin glass plate. The corresponding traversing time of photons isn't negative as the phase time either. We provide an experimental method to test and verify the proposed traversing time. [WT5HZ]

Acta Sinica Quantum Optica•Jan 1, 2001•0 citations

Time-dependent versus time-independent probabilities of transmission and reflection of a quantum particle incident upon a step potential and a square potential well

Mark R. A. Shegelski, Kevin Malmgren, Logan Salayka-Ladouceur

We investigate the transmission and reflection of a quantum particle incident upon a step potential decrease and a square well. The probabilities of transmission and reflection using the time-independent Schrödinger equation and also the time-dependent Schrödinger equation are in excellent agreement. We explain why the probabilities agree so well. In doing so, we make use of an exact analytical expression for the square well for time-dependent transmission and reflection, which reveals additional interesting and unexpected results. One such result is that transmission of a wave packet can occur with the probability of transmission depending weakly on the initial spread of the packet. The explanations and the additional results will be of interest to instructors of and students in upper year undergraduate quantum mechanics courses.

Canadian Journal of Physics•Oct 2, 2015•1 citation

Scattering a quantum particle on the potential step: Characteristic times for transmission and reflection

Nikolay Leonidovich Chuprikov

We present a new model of scattering a quantum particle on the potential step, which reconstructs the prehistory of the subensembles of transmitted and reflected particles by their final states. Unlike the conventional one this model predicts the existence of a transitional spatial region behind the potential step where the probability to find reflected particles is nonzero and the average velocity of transmitted particles monotonously varies between asymptotic values. For both subprocesses we define the dwell and asymptotic group times.

arXiv:1304.5179•Apr 18, 2013•0 citations

Quantum reflection in the linearly downward potential

N Chamnan, Boonlit Krunavakarn

In this work, the motion of a particle in one dimension under the influence of the linearly downward potential well is studied within the context of the non-relativistic quantum mechanics. The attention is paid on the paradoxical phenomenon of the reflection of a particle that is in contrast between classical and quantum physics. Classically, the reflection effect occurs only at a potential barrier. To demonstrate such counter-intuitive phenomenon, the Schrödinger equation is solved to obtain the reflection coefficient in the scattering state by considering an incident particle that is represented by a monochromatic plane wave having an energy E > 0, propagates freely from left to right, pass through the potential well. The continuity conditions at boundaries give the desired result that is expressed in terms of the Airy functions which depends on the incident energy E, the strength jV 0 j and the range L of the well. The value of the reflection coefficient R lies in the interval 0 < R < 1, and its behavior is the decreasing function with respect to the range L.

Journal of Physics Conference Series•Sep 1, 2017•1 citation
To understand the physical meaning of phase time further more, we discuss the reflection phase time of quantum-particles passing though a potential well It is shown that the reflection phase time is equal to the transmission phase time in value and negative under certain conditions for a square potential well by analyzing While quantum-particles passing through the potential well, we think that this course can be described only with the velocity of energy of quantum mechanics whether or not they are reflected or transmitted eventually
Introduction In classical physics it is meaningful to ask the question, ‘How much time does a particle take to pass through a given region?’ The interesting question in quantum mechanics is: does a particle take a definite time to tunnel through a classically forbidden region? The question has been debated ever since the idea that there was such a time in quantum theory was first put forward by MacColl way back in 1932 [253]. A plethora of times has since then been proposed, and the answer seems to depend on the interpretation of quantum mechanics one uses. A reliable answer is clearly of great importance for the design of high-frequency quantum devices, tunnelling phenomena (as, for example, in scanning tunneling microscopy), nuclear and chemical reactions and, of course, for purely conceptual reasons. Most of the controversies centre around simple and intuitive notions in idealized one-dimensional models in a scattering configuration in which a particle (usually represented by a wave packet) is incident on a potential barrier localized in the interval [ a, b ]. Three kinds of time have been defined in this context. One, called the transmission time τ T ( a, b ), is the average time spent within the barrier region by the particles that are eventually transmitted. Similarly, the reflection time τ R ( a, b ) is the average time spent within the barrier region by the particles that are eventually reflected.
A physically meaningful speed-the velocity of energy is used, which is similar to the energy speed in electromagnetism, to describe the process of particles passing through a potential well. It is shown that the corresponding traversing time of particles isn't negative as the phase time, which is negative under certain conditions. This speed can also describe the process of photons travelling through a non-dispersing thin glass plate. The corresponding traversing time of photons isn't negative as the phase time either. We provide an experimental method to test and verify the proposed traversing time. [WT5HZ]
We investigate the transmission and reflection of a quantum particle incident upon a step potential decrease and a square well. The probabilities of transmission and reflection using the time-independent Schrödinger equation and also the time-dependent Schrödinger equation are in excellent agreement. We explain why the probabilities agree so well. In doing so, we make use of an exact analytical expression for the square well for time-dependent transmission and reflection, which reveals additional interesting and unexpected results. One such result is that transmission of a wave packet can occur with the probability of transmission depending weakly on the initial spread of the packet. The explanations and the additional results will be of interest to instructors of and students in upper year undergraduate quantum mechanics courses.
We present a new model of scattering a quantum particle on the potential step, which reconstructs the prehistory of the subensembles of transmitted and reflected particles by their final states. Unlike the conventional one this model predicts the existence of a transitional spatial region behind the potential step where the probability to find reflected particles is nonzero and the average velocity of transmitted particles monotonously varies between asymptotic values. For both subprocesses we define the dwell and asymptotic group times.
In this work, the motion of a particle in one dimension under the influence of the linearly downward potential well is studied within the context of the non-relativistic quantum mechanics. The attention is paid on the paradoxical phenomenon of the reflection of a particle that is in contrast between classical and quantum physics. Classically, the reflection effect occurs only at a potential barrier. To demonstrate such counter-intuitive phenomenon, the Schrödinger equation is solved to obtain the reflection coefficient in the scattering state by considering an incident particle that is represented by a monochromatic plane wave having an energy E > 0, propagates freely from left to right, pass through the potential well. The continuity conditions at boundaries give the desired result that is expressed in terms of the Airy functions which depends on the incident energy E, the strength jV 0 j and the range L of the well. The value of the reflection coefficient R lies in the interval 0 < R < 1, and its behavior is the decreasing function with respect to the range L.