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

Bulletin of the Russian Academy of Sciences Physics

Penetration of Waves and Particles through Porous Structures

Г. М. Филиппов, В. А. Александров, I. V. Lysova, А. В. Степанов

Published Feb 1, 2018• 2 citations
Publisher

Abstract

The penetration of quantum and classical charged particles through porous films is investigated. The passage of quantum particles is analyzed by numerically solving the Schrödinger equation. The force of polarization acting on a charge is calculated by means of classical electrodynamics. The possibility of perforating thin films is analyzed.

DOI
10.3103/s1062873818020107

Related papers

Features of Quantum-Particle Propagation through Porous Structures

Г. М. Филиппов, A. S. Sabirov, В. А. Александров +1 more

Abstrtact The propagation of wave packets of quantum particles through porous structures in thin semi-transparent films is studied. Numerical solution of the nonstationary Schrödinger equation is used in two-dimensional (for slits) and three-dimensional (round holes) cases. The transmission coefficient of quantum particles is compared with that of classical particles with the same density distribution. The vortex motion of the flux density having a hydrodynamic analog is studied. A variant of the “quantum caustic” is considered upon scattering of the particle wave packet at an obstacle.

Journal of Surface Investigation X-ray Synchrotron and Neutron Techniques•Nov 1, 2020•2 citations

Penetration of Particles through Multi-Barrier Systems

Michael A. Bubenchikov, Aleksey Mikhaylovich BUBENCHIKOV, Либин Эдуард Ефимович +1 more

The paper gives a theoretical justification for the effect of increasing permeability of ultra-thin membranes by altering their internal material structure, namely through the process of creating one or two energy voids within the permeable layer. An effective computing technology for solving the stationary Schrödinger equation is also described.

MATEC Web of Conferences•Jan 1, 2016•0 citations

Wave Function Penetration, Tunneling, and Quantum Wells

Uri Peskin

Scanning tunneling microscopy is introduced as an analytic tool for characterizing nanostructures and dynamics on the nanoscale. To analyze the underlying tunneling phenomenon, the Schrödinger equation is solved for a particle confined between finite potential energy steps. For a single potential energy well, the proper solutions to the Schrödinger equation are similar to those of a particle in an infinite box, except for the emerging “tails” of the stationary wave functions in the “classically forbidden” regions of the external confining potentials. For a symmetric double well potential, wave function penetration of the stationary solutions manifests in their even distribution among the wells. An attempt to localize the particle in one of them would lead to periodic oscillations between the wells, as if the particle can “tunnel” under the separating energy barrier. The wave function penetration and tunneling phenomena are discussed also in relation to energy band formation in periodic lattices.

Cambridge University Press eBooks•May 11, 2023•0 citations

Numerical Analysis of Schrödinger Equations: Energy Structure and Particle Dynamics in a Potential

Magdalena Cieślik

Quantum mechanics describes phenomena that are key to understanding processes that cannot be explained by classical physics. This paper analyzes the behavior of particles in the presence of a potential barrier through numerical solutions to both time-dependent and time-independent Schrödinger equations. These results enabled a detailed understanding of the energy structure and temporal dynamics of wave functions, including the phenomenon of quantum tunneling. The obtained data have a wide range of applications in technology: from semiconductor devices to quantum computing.

Alcumena. Pismo Interdyscyplinarne•Oct 2, 2024•0 citations

Quantum Wave Mechanics as the Magnetic Interaction of Dirac Particles

David C. Lush

It is shown that a wave mechanical quantum theory can be derived from relativistic classical electrodynamics, as a feature of the magnetic interaction of Dirac particles modeled as relativistically circulating point charges. The magnetic force between two classical point charges, each undergoing relativistic circulatory motion of small radius compared to the separation between their centers of circulation, and assuming a time-symmetric electromagnetic interaction, is modulated by a factor that behaves similarly to the Schrödinger wavefunction. The magnetic force between relativistically-circulating charges has been shown previously to have a radially-directed inverse-square part of similar strength to the Coulomb force, and sinusoidally modulated by the phase difference of the charges' circulatory motions. The magnetic force modulation in the case of relatively moving centers of charge circulation solves an equation formally identical to the time-dependent free-particle Schrödinger equation, apart from a factor of two on the partial time derivative term. Considering motion in a time-independent potential obtains that the modulation also satisfies an equation formally similar to the time-independent Schrodinger equation. Using a formula for relativistic rest energy advanced by Osiak, the time-independent Schrödinger equation is solved exactly by the resulting modulation function. The significance of the quantum mechanical wavefunction follows straightforwardly from these observations. After considering the modification of Wheeler-Feynman absorber theory required by the adoption of Minkowski-Osiak relativity, the model is extended to obtain the full complex Schrödinger wavefunction.

arXiv:1609.04446•Sep 15, 2016•1 citation

A Simple Treatment of Potential Barrier Penetration

Bernard L. Cohen

It is pointed out that the penetration of a particle through a potential barrier may be understood as a climb over the barrier during one of the energy fluctuations expected from the uncertainty principle, rather than as a “tunneling” under the barrier. A method of obtaining the quantitative result with this model is presented.

American Journal of Physics•Feb 1, 1965•21 citations
The penetration of quantum and classical charged particles through porous films is investigated. The passage of quantum particles is analyzed by numerically solving the Schrödinger equation. The force of polarization acting on a charge is calculated by means of classical electrodynamics. The possibility of perforating thin films is analyzed.
Abstrtact The propagation of wave packets of quantum particles through porous structures in thin semi-transparent films is studied. Numerical solution of the nonstationary Schrödinger equation is used in two-dimensional (for slits) and three-dimensional (round holes) cases. The transmission coefficient of quantum particles is compared with that of classical particles with the same density distribution. The vortex motion of the flux density having a hydrodynamic analog is studied. A variant of the “quantum caustic” is considered upon scattering of the particle wave packet at an obstacle.
Scanning tunneling microscopy is introduced as an analytic tool for characterizing nanostructures and dynamics on the nanoscale. To analyze the underlying tunneling phenomenon, the Schrödinger equation is solved for a particle confined between finite potential energy steps. For a single potential energy well, the proper solutions to the Schrödinger equation are similar to those of a particle in an infinite box, except for the emerging “tails” of the stationary wave functions in the “classically forbidden” regions of the external confining potentials. For a symmetric double well potential, wave function penetration of the stationary solutions manifests in their even distribution among the wells. An attempt to localize the particle in one of them would lead to periodic oscillations between the wells, as if the particle can “tunnel” under the separating energy barrier. The wave function penetration and tunneling phenomena are discussed also in relation to energy band formation in periodic lattices.
Quantum mechanics describes phenomena that are key to understanding processes that cannot be explained by classical physics. This paper analyzes the behavior of particles in the presence of a potential barrier through numerical solutions to both time-dependent and time-independent Schrödinger equations. These results enabled a detailed understanding of the energy structure and temporal dynamics of wave functions, including the phenomenon of quantum tunneling. The obtained data have a wide range of applications in technology: from semiconductor devices to quantum computing.
It is shown that a wave mechanical quantum theory can be derived from relativistic classical electrodynamics, as a feature of the magnetic interaction of Dirac particles modeled as relativistically circulating point charges. The magnetic force between two classical point charges, each undergoing relativistic circulatory motion of small radius compared to the separation between their centers of circulation, and assuming a time-symmetric electromagnetic interaction, is modulated by a factor that behaves similarly to the Schrödinger wavefunction. The magnetic force between relativistically-circulating charges has been shown previously to have a radially-directed inverse-square part of similar strength to the Coulomb force, and sinusoidally modulated by the phase difference of the charges' circulatory motions. The magnetic force modulation in the case of relatively moving centers of charge circulation solves an equation formally identical to the time-dependent free-particle Schrödinger equation, apart from a factor of two on the partial time derivative term. Considering motion in a time-independent potential obtains that the modulation also satisfies an equation formally similar to the time-independent Schrodinger equation. Using a formula for relativistic rest energy advanced by Osiak, the time-independent Schrödinger equation is solved exactly by the resulting modulation function. The significance of the quantum mechanical wavefunction follows straightforwardly from these observations. After considering the modification of Wheeler-Feynman absorber theory required by the adoption of Minkowski-Osiak relativity, the model is extended to obtain the full complex Schrödinger wavefunction.