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

Physical Review A

Specific case of the boundary quantum phase effect

Mohsen Razavy

Published Jul 1, 1989• 13 citations
Publisher

Abstract

It is shown that the wave function of a particle passing through a constriction experiences a phase shift that is dependent on the geometrical shape of the boundary. For a separable problem the change in the spatial boundary in one of the coordinates brings about a nonlocal potential in the wave equation for the other coordinate. This feature has been studied by solving the Schr\"odinger equation in the elliptic cylinder coordinates.

DOI
10.1103/physreva.40.1

Related papers

Nonlocal effects induced by the phase of the Schr\"odinger wavefunction for a particle in a cavity with moving boundaries

Mordecai Waegell, A. Matzkin

We investigate the dynamics of a particle in a confined periodic system --- a time-dependent oscillator confined by infinitely high and moving walls --- and focus on the evolution of the phase of the wavefunction. It is shown that for some specific initial states in this potential, the phase evolves nonlocally. We further elaborate a thought experiment devised to detect this form of single-particle nonlocality. We point out that within the non-relativistic formalism based on the Schr\"odinger equation (SE), detecting this form of nonlocality can give rise to signaling. We believe this effect is an artifact, but the standard relativistic corrections to the SE do not appear to fix it. Specific illustrations are given, with analytical results in the adiabatic approximation, and numerical computations to show that contributions from high-energy states (corresponding to superluminal velocities) are negligible.

•Dec 12, 2019•0 citations

Some exact results for the Schrödinger wave equation with a time-dependent potential

Joel F. Campbell

The time-dependent Schrödinger equation with a time-dependent delta function potential is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation of the Volterra type. It is shown that by knowing the wavefunction at the origin, one may derive the wavefunction everywhere. Thus, the problem is reduced from a PDE in two variables to an integral equation in one. These results are used to compare adiabatic versus sudden changes in the potential. It is shown that adiabatic changes in the potential lead to the conservation of the normalization of the probability density.

Journal of Physics A Mathematical and Theoretical•Aug 24, 2009•26 citations

ANALYTICAL SOLUTION OF SCHRÖDINGER EQUATION FOR YUKAWA POTENTIAL WITH VARIABLE MASS IN TOROIDAL COORDINATE USING SUPERSYMMETRIC QUANTUM MECHANICS

Suci Faniandari, Suparmi Suparmi, C. Cari

Schrodinger equation on a toroidal coordinate was proposed in theoretical physics to get the information and the behavior of the system of particle. It was solved just recently in case of a charged scalar particle interacting with a uniform magnetic field, a uniform electric field, and a neutral charge constrained to the surface. The methodology used in the referred work was to solve the Schrodinger equation using an approach outlined in the Whittaker-Watson treatise, which deals with an infinite-dimensional eigenvalue problem and specific particular values of the applied field for eigenfunction problem. In contrast, in the quantum mechanical problem, one had an infinite-dimensional generalized eigenvalue problem. This study aimed to obtain the non-relativistic energy eigenvalue and the radial wave function of the Schrodinger equation under the influence of Yukawa potential. The Supersymmetric Quantum Mechanics (SUSY QM) method was used as a basis to tackle the primary objective of this paper to study the problem of a particle with variable mass in toroidal coordinate. The proper super potential was used to deal with the hyperbolic form of effective potential, and the energy spectra were calculated for different quantum numbers, potential depth, and potential parameters. The radial wave function equation for ground and excited state were obtained. The results showed that the increasing value of the quantum numbers caused the energy spectra of the system to increase to the highest value when the quantum number was equal to the potential parameter, which means the most effective energy value was produced, then it was decreased afterward. While the energy value did not depend on the change of the potential parameter. This property could be used to produce this equation as an application of the previous results, the Schrödinger eigenfunction was used as the starting points to solve the other equation in the same geometrical setting and potential.

PERIÓDICO TCHÊ QUÍMICA•Jul 20, 2020•1 citation

Single particle nonlocality, geometric phases and time-dependent boundary conditions

A. Matzkin

Abstract We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We discuss earlier claims according to which the quantum state of a particle remaining localized at the center of an infinite well with moving walls would be specifically modified by the change in boundary conditions due to the wall’s motion. We first prove that the evolution of an initially localized Gaussian state is not affected nonlocally by a linearly moving wall: as long as the quantum state has negligible amplitude near the wall, the boundary motion has no effect. This result is further extended to related confined time-dependent oscillators in which the boundary’s motion is known to give rise to geometric phases: for a Gaussian state remaining localized far from the boundaries, the effect of the geometric phases is washed out and the particle dynamics shows no traces of a nonlocal influence that would be induced by the moving boundaries.

arXiv:1706.08617•Journal of Physics A Mathematical and Theoretical•Feb 6, 2018•8 citations

ANALYSIS OF ENERGY AND WAVE FUNCTIONS AND THE THERMODYNAMICS PROPERTIES OF THE 6-DIMENSIONAL SCHRODINGER EQUATION UNDER DOUBLE RING-SHAPE OSCILLATOR (DRSO) AND MANNING-ROSEN POTENTIALS USING SUSY QM METHOD

Dedy A. Bilaut, Suparmi Suparmi, C. Cari +1 more

The exact solutions of the Schrodinger equations (SE) in the D-dimensional coordinate system have attracted the attention of many theoretical researchers in branches of quantum physics and quantum chemistry. The energy eigenvalues and the wave function are the solutions of the Schrodinger equation that implicitly represents the behavior of a quantum mechanical system. This study aimed to obtain the eigenvalues, wave functions, and thermodynamic properties of the 6-Dimensional Schrodinger equation under Double Ring-Shaped Oscillator (DRSO) and Manning-Rosen potential. The variable separation method was applied to reduce the one 6-Dimensional Schrodinger equation depending on radial and angular non-central potential into five onedimensional Schrodinger equations: one radial and five angular Schrodinger equations. Each of these onedimensional Schrodinger equations was solved using the SUSY QM method to obtain one eigenvalue and one wave function of the radial part, five eigenvalues, and five angular wave functions angular part. Some thermodynamic properties such, the vibrational mean energy 𝑈, vibrational specific heat 𝐶, vibrational free energy 𝐹, and vibrational entropy 𝑆, were obtained using the radial energy equations. The results showed that except the 𝑛𝑙1, all increment of angular quantum number decreases the energy values. Increments of all potential parameter increase the energy values. Increment of angular quantum number and potentials parameter increases the amplitude and shifts the wave functions to the left. However, the increment of 𝑛𝑙1, 𝛼, 𝜎, and 𝜌 decrease the amplitude and shift wavefunctions to the right. Moreover, the vibrational mean energy 𝑈 and free energy 𝐹 increased as the increasing value of potentials parameters, where the ω parameter has the dominant effect than the other parameters. The vibrational specific heat 𝐶 and entropy 𝑆 affected only by the 𝜔 parameter, where 𝐶 and 𝑆 decreased as the increase of 𝜔.

PERIÓDICO TCHÊ QUÍMICA•Dec 20, 2020•0 citations

Boundary-induced perturbations

J. R. Morris

A simple quantum mechanical system consisting of a particle in a one-dimensional impenetrable box is considered in a situation wherein the wavefunction is subjected to moving boundary conditions. A method of approximating the wavefunction is presented and applied to a simple example.

American Journal of Physics•Jan 1, 1988•4 citations
It is shown that the wave function of a particle passing through a constriction experiences a phase shift that is dependent on the geometrical shape of the boundary. For a separable problem the change in the spatial boundary in one of the coordinates brings about a nonlocal potential in the wave equation for the other coordinate. This feature has been studied by solving the Schr"odinger equation in the elliptic cylinder coordinates.
We investigate the dynamics of a particle in a confined periodic system --- a time-dependent oscillator confined by infinitely high and moving walls --- and focus on the evolution of the phase of the wavefunction. It is shown that for some specific initial states in this potential, the phase evolves nonlocally. We further elaborate a thought experiment devised to detect this form of single-particle nonlocality. We point out that within the non-relativistic formalism based on the Schr\"odinger equation (SE), detecting this form of nonlocality can give rise to signaling. We believe this effect is an artifact, but the standard relativistic corrections to the SE do not appear to fix it. Specific illustrations are given, with analytical results in the adiabatic approximation, and numerical computations to show that contributions from high-energy states (corresponding to superluminal velocities) are negligible.
The time-dependent Schrödinger equation with a time-dependent delta function potential is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation of the Volterra type. It is shown that by knowing the wavefunction at the origin, one may derive the wavefunction everywhere. Thus, the problem is reduced from a PDE in two variables to an integral equation in one. These results are used to compare adiabatic versus sudden changes in the potential. It is shown that adiabatic changes in the potential lead to the conservation of the normalization of the probability density.
Schrodinger equation on a toroidal coordinate was proposed in theoretical physics to get the information and the behavior of the system of particle. It was solved just recently in case of a charged scalar particle interacting with a uniform magnetic field, a uniform electric field, and a neutral charge constrained to the surface. The methodology used in the referred work was to solve the Schrodinger equation using an approach outlined in the Whittaker-Watson treatise, which deals with an infinite-dimensional eigenvalue problem and specific particular values of the applied field for eigenfunction problem. In contrast, in the quantum mechanical problem, one had an infinite-dimensional generalized eigenvalue problem. This study aimed to obtain the non-relativistic energy eigenvalue and the radial wave function of the Schrodinger equation under the influence of Yukawa potential. The Supersymmetric Quantum Mechanics (SUSY QM) method was used as a basis to tackle the primary objective of this paper to study the problem of a particle with variable mass in toroidal coordinate. The proper super potential was used to deal with the hyperbolic form of effective potential, and the energy spectra were calculated for different quantum numbers, potential depth, and potential parameters. The radial wave function equation for ground and excited state were obtained. The results showed that the increasing value of the quantum numbers caused the energy spectra of the system to increase to the highest value when the quantum number was equal to the potential parameter, which means the most effective energy value was produced, then it was decreased afterward. While the energy value did not depend on the change of the potential parameter. This property could be used to produce this equation as an application of the previous results, the Schrödinger eigenfunction was used as the starting points to solve the other equation in the same geometrical setting and potential.
Abstract We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We discuss earlier claims according to which the quantum state of a particle remaining localized at the center of an infinite well with moving walls would be specifically modified by the change in boundary conditions due to the wall’s motion. We first prove that the evolution of an initially localized Gaussian state is not affected nonlocally by a linearly moving wall: as long as the quantum state has negligible amplitude near the wall, the boundary motion has no effect. This result is further extended to related confined time-dependent oscillators in which the boundary’s motion is known to give rise to geometric phases: for a Gaussian state remaining localized far from the boundaries, the effect of the geometric phases is washed out and the particle dynamics shows no traces of a nonlocal influence that would be induced by the moving boundaries.
The exact solutions of the Schrodinger equations (SE) in the D-dimensional coordinate system have attracted the attention of many theoretical researchers in branches of quantum physics and quantum chemistry. The energy eigenvalues and the wave function are the solutions of the Schrodinger equation that implicitly represents the behavior of a quantum mechanical system. This study aimed to obtain the eigenvalues, wave functions, and thermodynamic properties of the 6-Dimensional Schrodinger equation under Double Ring-Shaped Oscillator (DRSO) and Manning-Rosen potential. The variable separation method was applied to reduce the one 6-Dimensional Schrodinger equation depending on radial and angular non-central potential into five onedimensional Schrodinger equations: one radial and five angular Schrodinger equations. Each of these onedimensional Schrodinger equations was solved using the SUSY QM method to obtain one eigenvalue and one wave function of the radial part, five eigenvalues, and five angular wave functions angular part. Some thermodynamic properties such, the vibrational mean energy 𝑈, vibrational specific heat 𝐶, vibrational free energy 𝐹, and vibrational entropy 𝑆, were obtained using the radial energy equations. The results showed that except the 𝑛𝑙1, all increment of angular quantum number decreases the energy values. Increments of all potential parameter increase the energy values. Increment of angular quantum number and potentials parameter increases the amplitude and shifts the wave functions to the left. However, the increment of 𝑛𝑙1, 𝛼, 𝜎, and 𝜌 decrease the amplitude and shift wavefunctions to the right. Moreover, the vibrational mean energy 𝑈 and free energy 𝐹 increased as the increasing value of potentials parameters, where the ω parameter has the dominant effect than the other parameters. The vibrational specific heat 𝐶 and entropy 𝑆 affected only by the 𝜔 parameter, where 𝐶 and 𝑆 decreased as the increase of 𝜔.