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

American Journal of Physics

Boundary-induced perturbations

J. R. Morris

Published Jan 1, 1988• 4 citations
Publisher

Abstract

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.
DOI
10.1119/1.15429

Related papers

Iterative boundary perturbation method for enclosed one-dimensional quantum systems

Jerzy Górecki, Bryson Brown

A modification of the boundary perturbation theory of Hull and Julius (1950) is proposed which lends itself to iterative solution. The method may be applied to both finite and infinite box potentials. For enclosed quantum systems described by one-dimensional Schrodinger equations it leads to the exact energy and wavefunction.

Journal of Physics B Atomic and Molecular Physics•Nov 28, 1987•24 citations

Approach to perturbation theory for box models

Francisco Marcelo Fernández

We generalize a recently developed perturbation approach [F. M. Fern\'andez and E. A. Castro, Phys. Rev. A 46, 7288 (1992)], extending its applicability to a wider variety of separable quantum-mechanical problems. As an illustrative example, we consider a particle in a one-dimensional box with a finite potential wall perturbed by a linear potential and obtain the perturbation corrections to the wave function and energy of an arbitrary state in terms of the corresponding unperturbed quantities.

Physical Review A•Jul 1, 1993•5 citations

Problem of Perturbed Boundary Condition in Quantum Mechanics

S Sen Gupta, H Mukhopadhyay

Problem of perturbed boundary condition is reduced to an equivalent problem of perturbation potential with the introduction of a deformed coordinate system. The method is applied to determine the energy of a nucleon in a rigid ellipsoidal box.

Proceedings of the Physical Society•Feb 1, 1958•2 citations

On the repulsive nature of the Dirichlet boundaries in the confined atom problem

Vladimir I. Pupyshev

An atom in a box with penetrable or impenetrable potential walls is shown analytically to move under the influence of the repulsive forces from the boundaries of the cavity when all the atom-medium interactions are described by the Dirichlet boundary conditions or effective one-particle `box' potentials. Simple geometrical methods allow one to find the energetically optimal position of the atom in the cavity. For instance, the ground state energy of the hydrogen atom is proved to be minimal when the nucleus is situated at the centre of the cube or sphere. Some applications for molecules are also mentioned.

Journal of Physics B Atomic Molecular and Optical Physics•Mar 1, 2000•20 citations

Quantum-mechanical systems restricted by impenetrable barriers studied by a perturbation method

Igor Gonda, B. F. Gray

A systematic perturbation method to calculate the explicit dependence of energy on the position of the repulsive barrier (or barriers) in one-dimensional non-degenerate systems is presented. The method is also capable of dealing with anisotropic shifts of the boundaries. Two simple applications illustrate the general principles (particle in a box and compression of the ground state of the hydrogen atom).

Journal of the Chemical Society Faraday Transactions 2 Molecular and Chemical Physics•Jan 1, 1975•18 citations

Boundary Conditions and Wave Functions of the Particle in a Box

Lan Chen, Hongwei Sun, Cheng-Ming LAI

University Chemistry•Jan 1, 2017•0 citations
We generalize a recently developed perturbation approach [F. M. Fern\'andez and E. A. Castro, Phys. Rev. A 46, 7288 (1992)], extending its applicability to a wider variety of separable quantum-mechanical problems. As an illustrative example, we consider a particle in a one-dimensional box with a finite potential wall perturbed by a linear potential and obtain the perturbation corrections to the wave function and energy of an arbitrary state in terms of the corresponding unperturbed quantities.
An atom in a box with penetrable or impenetrable potential walls is shown analytically to move under the influence of the repulsive forces from the boundaries of the cavity when all the atom-medium interactions are described by the Dirichlet boundary conditions or effective one-particle `box' potentials. Simple geometrical methods allow one to find the energetically optimal position of the atom in the cavity. For instance, the ground state energy of the hydrogen atom is proved to be minimal when the nucleus is situated at the centre of the cube or sphere. Some applications for molecules are also mentioned.