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

Acta Physica Sinica (Overseas Edition)

Berry phases in the quantum state of the isotropic harmonic oscillator with time-dependent frequency and boundary conditions

Liu Deng-yun

Published Jan 1, 1999• 5 citations
Publisher

Abstract

The problem of the isotopic harmonic oscillator of time-dependent frequency confined in a spherical box with time-dependent radius is studied. We show that the exact solution and the Lewis invariant operator can be obtained by performing two consecutive gauge transformations on the time-dependent Schrödinger equation. On the basis of the exact solution the non-adiabatic Berry phases for the system are calculated.

DOI
10.1088/1004-423x/8/1/001

Related papers

THE BERRY PHASE OF THE QUANTUM STATE OF A HARMONIC OSCILLATOR WITH TIME DEPENDENT FREQUENCY AND BOUNDARY CONDITIONS

Eng Y

Abstract The problem of a harmonic oscillator of time dependent frequency confined in a one dimensional infinite square well with a moving wall is studied.It is shown that the exact solution and the Lewis invariant operator of the system can be obtained by performing two consecutive gauge transformations on the time dependent Schrdinger equation.On the basis of the exact solution the Berry phases for the system are calculated by using the geometric concepts such as the geometric distance and geometric length of the curve.

Acta Physica Sinica•Jan 1, 1998•0 citations

THE BERRY PHASE OF THE QUANTUM STATE OF A HARMONIC OSCILLATOR WITH TIME-DEPENDENT FREQUENCY AND BOUNDARY CONDITIONS

Liu Deng-yun, 山西师范大学物理系，临汾 041004

The problem of a harmonic oscillator of time-dependent frequency confined in a one-dimensional infinite square well with a moving wall is studied.It is shown that the exact solution and the Lewis invariant operator of the system can be obtained by performing two consecutive gauge transformations on the time-dependent Schrdinger equation.On the basis of the exact solution the Berry phases for the system are calculated by using the geometric concepts such as the geometric distance and geometric length of the curve.

Acta Physica Sinica•Jan 1, 1998•2 citations

Gauge transformation approach to the exact solution of a generalized harmonic oscillator

Fuli Li, Shun-Jin Wang, A. Weiguny +1 more

The exact solution and the invariant operator of a generalized harmonic oscillator are obtained by performing three consecutive gauge transformations on the time-dependent Schrodinger equation. In contrast to previous results, they depend only on solutions of a linear differential equation for the associated classical harmonic oscillator. Non-adiabatic and adiabatic Berry phases for the system are calculated on the basis of the exact solution.

Journal of Physics A Mathematical and General•Feb 7, 1994•39 citations

LEWIS-RIESENFELD PHASES AND BERRY PHASES IN THEQUANTUM SYSTEM OF TIME-DEPENDENT HARMONICOSCILLATOR WITH A MOVING BOUNDARY

Li Ling, Bo‐Zang Li, Liang Jiu-Qing +1 more

Using the Lewis-Riesenfeld′s quantum invariant theory,the Lewis-Riesenfeld phases for a time-dependent frequency harmonic oscillator,which is confined in an infinite well with a moving wall,are calculated.We find that the geometric part of the Lewis-Riesenfeld phases are identical with the “non-adiabatic Berry phases” described by D.Y.Liu in Acta Phys.Sin.It may be important that our results,at least for the system with a sinusoidally oscillating boundary,do not show any non-trivial Berry phase acquired.

Acta Physica Sinica•Jan 1, 2001•1 citation

LEWIS–RIESENFELD PHASES AND BERRY PHASES FOR THE HARMONIC OSCILLATOR WITH TIME-DEPENDENT FREQUENCY AND BOUNDARY CONDITIONS

Ling Li, Bo‐Zang Li

We use Lewis and Riesenfeld's quantum invariant theory to calculate the Lewis–Riesenfeld phases for a time-dependent frequency harmonic oscillator that is confined between a fixed boundary and a moving one. We also discuss the Berry phase for the system with a sinusoidally oscillating boundary.

International Journal of Modern Physics B•Apr 20, 2003•3 citations

TIME DEPENDENT BOUNDARY CONDITIONS AND BERRY PHASE

Liu Deng-yun, 山西师范大学物理系,临汾041004

For a quantum system with time dependent boundary conditions, it is shown that the ef-fective Hamiltonian can be constructed in a simple way without any geometric treatemnt. In this paper the effective Hamiltonian, constructed in the above way, of quantum particle in a spherical box of varying radius is used to calculate the Berry phase of the wave function. We found that the effective Hamiltonian and original one are formally related with a static gauge transformation, the quantum states of the two Hamiltonians differ by a Berry phase.

Acta Physica Sinica•Jan 1, 1993•2 citations
The problem of the isotopic harmonic oscillator of time-dependent frequency confined in a spherical box with time-dependent radius is studied. We show that the exact solution and the Lewis invariant operator can be obtained by performing two consecutive gauge transformations on the time-dependent Schrödinger equation. On the basis of the exact solution the non-adiabatic Berry phases for the system are calculated.
Abstract The problem of a harmonic oscillator of time dependent frequency confined in a one dimensional infinite square well with a moving wall is studied.It is shown that the exact solution and the Lewis invariant operator of the system can be obtained by performing two consecutive gauge transformations on the time dependent Schrdinger equation.On the basis of the exact solution the Berry phases for the system are calculated by using the geometric concepts such as the geometric distance and geometric length of the curve.
The problem of a harmonic oscillator of time-dependent frequency confined in a one-dimensional infinite square well with a moving wall is studied.It is shown that the exact solution and the Lewis invariant operator of the system can be obtained by performing two consecutive gauge transformations on the time-dependent Schrdinger equation.On the basis of the exact solution the Berry phases for the system are calculated by using the geometric concepts such as the geometric distance and geometric length of the curve.
Using the Lewis-Riesenfeld′s quantum invariant theory,the Lewis-Riesenfeld phases for a time-dependent frequency harmonic oscillator,which is confined in an infinite well with a moving wall,are calculated.We find that the geometric part of the Lewis-Riesenfeld phases are identical with the “non-adiabatic Berry phases” described by D.Y.Liu in Acta Phys.Sin.It may be important that our results,at least for the system with a sinusoidally oscillating boundary,do not show any non-trivial Berry phase acquired.
For a quantum system with time dependent boundary conditions, it is shown that the ef-fective Hamiltonian can be constructed in a simple way without any geometric treatemnt. In this paper the effective Hamiltonian, constructed in the above way, of quantum particle in a spherical box of varying radius is used to calculate the Berry phase of the wave function. We found that the effective Hamiltonian and original one are formally related with a static gauge transformation, the quantum states of the two Hamiltonians differ by a Berry phase.