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

International Journal of Trend in Scientific Research and Development

Study on Transmission Probabilities for Some Rectangular Potential Barriers

Htay Yee, Thida Win Aye Aye Myint Kyaw Kyaw Naing, Aye Than Kyae

Published Aug 22, 2019• 1 citation
OpenAlex

Related papers

Tunnelling

Peter Joshua Atkins, Julio de Paula, Ronald Friedman

Contents The rectangular potential energy barrier 80 Brief illustration 10.1: Transmission probabilities for a rectangular barrier 83 The Eckart potential energy barrier 83 Brief illustration 10.2: Transmission probabilities for an Eckart barrier 84 The double-well potential 85 Brief illustration 10.3: The inversion...

Oxford University Press eBooks•Dec 12, 2013•0 citations

Computation of transmission probabilities for thin potential barriers with transmitted quantum trajectories

Chia‐Chun Chou

Physics Letters A•Jul 4, 2015•5 citations

Dynamic transmission and reflection phenomena for a time-dependent rectangular potential

D. L. Haavig, Ronald G. Reifenberger

The time-dependent Schr\"odinger equation is solved for a one-dimensional rectangular potential whose height changes sinusoidally in time. By using standard wave-matching techniques, dynamic transmission and reflection probabilities are found. It is shown that the flux transmitted through the barrier region is modulated in time at integer multiples of ${\ensuremath{\omega}}_{b}$, the angular frequency at which the potential oscillates. The results obtained for a delocalized plane wave incident on the barrier are extended by considering the interaction of a Gaussian wave packet with the oscillating potential barrier. The modulation of the transmitted and reflected probability density by the oscillating barrier is clearly demonstrated by a series of calculations performed to illustrate this interaction. These calculations also show that the probability density leaving the barrier region is composed of individual wave packets having different average velocities, a result which is a direct consequence of the transitions induced by the time-dependent potential barrier under consideration. Calculations are also performed which show that the flux transmitted across the potential barrier depends on the phase of the oscillating barrier at the time the incident Gaussian wave packet begins to interact with it. The results of these model calculations suggest that experiments properly designed to measure the transmission probability of a quantum particle as it escapes from a metal surface are likely to provide information about the time formation of the dynamic image potential.

Physical review. B, Condensed matter•Dec 15, 1982•47 citations

On the distribution of transmission and reflection times for a one dimensional barriers

C. Richard Leavens

Solid State Communications•Oct 1, 1988•17 citations

Analytic bounds on transmission probabilities

Petarpa Boonserm, Matt Visser

arXiv:0901.0944•Annals of Physics•Apr 14, 2010•37 citations

Quantum nature of proton transferring across one-dimensional potential fields*

Cheng Bi, Quan Chen, Wei Li +1 more

Proton transfer plays a key role in the applications of advanced energy materials as well as in the functionalities of biological systems. In this work, based on the transfer matrix method, we study the quantum effects of proton transfer in a series of one-dimensional (1D) model potentials and numerically calculate the quantum probability of transferring across single and double barriers (wells). In the case of single barriers, when the incident energies of protons are above the barrier height, the quantum oscillations in the transmission coefficients depend on the geometric shape of the barriers. It is found that atomic resonant tunneling (ART) not only presents in the rectangular single well and rectangular double barriers as expected, but also exists in the other types of potential wells and double barriers. For hetero-structured double barriers, there is no resonant tunneling in the classical forbidden zone, i.e., in the case when the incident energy (E i) is lower than the barrier height (E b). Furthermore, we have provided generalized analysis on the characteristics of transmission coefficients of hetero-structured rectangular double barriers.

Chinese Physics B•Jan 29, 2021•6 citations
The time-dependent Schr\"odinger equation is solved for a one-dimensional rectangular potential whose height changes sinusoidally in time. By using standard wave-matching techniques, dynamic transmission and reflection probabilities are found. It is shown that the flux transmitted through the barrier region is modulated in time at integer multiples of ${\ensuremath{\omega}}_{b}$, the angular frequency at which the potential oscillates. The results obtained for a delocalized plane wave incident on the barrier are extended by considering the interaction of a Gaussian wave packet with the oscillating potential barrier. The modulation of the transmitted and reflected probability density by the oscillating barrier is clearly demonstrated by a series of calculations performed to illustrate this interaction. These calculations also show that the probability density leaving the barrier region is composed of individual wave packets having different average velocities, a result which is a direct consequence of the transitions induced by the time-dependent potential barrier under consideration. Calculations are also performed which show that the flux transmitted across the potential barrier depends on the phase of the oscillating barrier at the time the incident Gaussian wave packet begins to interact with it. The results of these model calculations suggest that experiments properly designed to measure the transmission probability of a quantum particle as it escapes from a metal surface are likely to provide information about the time formation of the dynamic image potential.
Proton transfer plays a key role in the applications of advanced energy materials as well as in the functionalities of biological systems. In this work, based on the transfer matrix method, we study the quantum effects of proton transfer in a series of one-dimensional (1D) model potentials and numerically calculate the quantum probability of transferring across single and double barriers (wells). In the case of single barriers, when the incident energies of protons are above the barrier height, the quantum oscillations in the transmission coefficients depend on the geometric shape of the barriers. It is found that atomic resonant tunneling (ART) not only presents in the rectangular single well and rectangular double barriers as expected, but also exists in the other types of potential wells and double barriers. For hetero-structured double barriers, there is no resonant tunneling in the classical forbidden zone, i.e., in the case when the incident energy (E i) is lower than the barrier height (E b). Furthermore, we have provided generalized analysis on the characteristics of transmission coefficients of hetero-structured rectangular double barriers.