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Acta Physica Sinica

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

Eng Y

Published Jan 1, 1998• 0 citations
OpenAlex

Abstract

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.

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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

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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

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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

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
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.