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 Polonica A

Invariants for Time-Dependent Harmonic Oscillators from the Real Representation of Solution

Mai-Lin Liang, Z.G. Zhang, Bing Yuan

Published Mar 1, 2004• 1 citation
Publisher
DOI
10.12693/aphyspola.105.253

Related papers

Invariants for time-dependent harmonic oscillators from real representation of solution

Wu Chuang

The invariants for the time-dependent one-dimensional harmonic oscillator and the time-dependent two-dimensional harmonic oscillator in a static magnetic field are derived from the real representation of the exact solution to the equation of motion.Mathematically,the orthogonal functions invariant is the angular momentum of an isotropic time-dependent two-dimensional harmonic oscillator.Based on the invariants obtained here,the wave function for time-dependent two-dimensional harmonic oscillator in a static magnetic field in cylindrical coordinate is simply derived and the dynamical and geometrical phases are easily got by expressing the wave function as the superpositions of the wave functions of time-dependent two-dimensional harmonic oscillator in rectangular coordinate.

Journal of Shenyang Normal University•Jan 1, 2011•0 citations

On the time-dependent harmonic oscillator

Ettore Salusti B, Francesco Zirilli

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento•Nov 1, 1970•11 citations

Exact wave function of the time-dependent harmonic oscillator in the invariant representation

Feng Jin

The two quantum invariant operators are constructed from the time dependent Harmiltonian of the harmonic oscillator with an auxiliary condition. The solution of the Schrdinger equation for the system is derived by using these invariant operators.

College Physics•Jan 1, 2001•0 citations

Some remarks on the time-dependent harmonic oscillator

B. Bassetti, E. Montaldi, Mario Raciti

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento•Apr 1, 1982•4 citations

Time-Dependent Coupled Harmonic Oscillators: Classical and Quantum Solutions

Diego Ximenes Macedo, Ilde Guedes

WORLD SCIENTIFIC eBooks•Sep 28, 2014•0 citations

Gauge-covariant properties of a linear nonautonomous quantum system: time-dependent even and odd coherent states

L. F. Wei, Shun-Jin Wang, X. L. Lei

A new method for finding the dynamical invariant for a general time-dependent harmonic oscillator is proposed by making use of two linearly independent solutions to the classical equation of motion. It is shown that the dynamical invariant for different gauged Hamiltonians are connected by time-dependent gauge transformations. Therefore, the representation whose bases are the instantaneous eigenstates of the invariant operator is a good representation for the quantum nonautonomous system. In this representation, the wavefunction of the system is gauge covariant and thus any observable physical effect is naturally independent of the choice of gauged Hamiltonians. The exact even and odd coherent states for a time-dependent harmonic oscillator are constructed in terms of these gauge covariant bases. The harmonic oscillator with periodically varying frequency is treated as a demonstration of our general approach.

Journal of Physics A Mathematical and General•Jan 7, 2002•7 citations
The invariants for the time-dependent one-dimensional harmonic oscillator and the time-dependent two-dimensional harmonic oscillator in a static magnetic field are derived from the real representation of the exact solution to the equation of motion.Mathematically,the orthogonal functions invariant is the angular momentum of an isotropic time-dependent two-dimensional harmonic oscillator.Based on the invariants obtained here,the wave function for time-dependent two-dimensional harmonic oscillator in a static magnetic field in cylindrical coordinate is simply derived and the dynamical and geometrical phases are easily got by expressing the wave function as the superpositions of the wave functions of time-dependent two-dimensional harmonic oscillator in rectangular coordinate.
A new method for finding the dynamical invariant for a general time-dependent harmonic oscillator is proposed by making use of two linearly independent solutions to the classical equation of motion. It is shown that the dynamical invariant for different gauged Hamiltonians are connected by time-dependent gauge transformations. Therefore, the representation whose bases are the instantaneous eigenstates of the invariant operator is a good representation for the quantum nonautonomous system. In this representation, the wavefunction of the system is gauge covariant and thus any observable physical effect is naturally independent of the choice of gauged Hamiltonians. The exact even and odd coherent states for a time-dependent harmonic oscillator are constructed in terms of these gauge covariant bases. The harmonic oscillator with periodically varying frequency is treated as a demonstration of our general approach.