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

Journal of Sichuan Normal University

The Time Dependent Particle Number Representation and the Adiabatic Quantum Phase of the Generalized Time Dependent Harmonic Oscillator and Its Time Dependent Coherent States

Hou Bang

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

In this paper, the annihilation and creation operators are defined directly for the generalized time dependent harmonic oscillator. And the time dependent particle number representation is constructed, in which the adiabatic quantum phase is obtained, the adiabatic time dependent coherent states are found, and the essential properties for the coherent states are also discussed.

Related papers

Even and Odd Coherent States for Time-Dependent Harmonic Oscillator

Lian-Fu Wei, Qingyi Yang, Shun-Jin Wang

The dynamical invariant for a general time-dependent harmonic oscillator is constructed by making use of two linearly independent solutions to the classical equation of motion. In terms of this dynamical invariant we define the time-dependent creation and annihilation operators and relevantly introduce even and odd coherent states for time-dependent harmonic oscillator. The mathematical and quantum statistical properties of these states are discussed in detail. The harmonic oscillator with periodically varying frequency is treated as a demonstration of our general approach.

Communications in Theoretical Physics•Jul 15, 2002•1 citation

Eigenstates of the higher powers of an annihilation operator for a time-dependent harmonic oscillator and their properties

Xiao-Hua Wang, Jin-Song Huang, Yu Liu +1 more

In the framework of dynamical invariant theory, we introduce the annihilation operator and creation operator for a time-dependent harmonic oscillator. The orthonormalized eigenstates of the operator are constructed, and their mathematical and quantum statistical properties are discussed in detail. Specifically, a particle moving in a Paul trap with periodically varying frequency is treated as an example to demonstrate the dynamical squeezing effects for the eigenstates of the operator .

Journal of Physics A Mathematical and Theoretical•Mar 3, 2010•0 citations

Generalized creation and annihilation operators via complex nonlinear Riccati equations

Dieter Schuch, Octavio Castaños, Óscar Rosas-Ortiz

Based on Gaussian wave packet solutions of the time-dependent Schrödinger equation, a generalization of the conventional creation and annihilation operators and the corresponding coherent states can be obtained. This generalization includes systems where also the width of the coherent states is time-dependent as they occur for harmonic oscillators with time-dependent frequency or systems in contact with a dissipative environment. The key point is the replacement of the frequency ω 0 that occurs in the usual definition of the creation/annihilation operator by a complex time-dependent function that fulfils a nonlinear Riccati equation. This equation and its solutions depend on the system under consideration and on the (complex) initial conditions. Formal similarities also exist with supersymmetric quantum mechanics. The generalized creation and annihilation operators also allow to construct exact analytic solutions of the free motion Schrödinger equation in terms of Hermite polynomials with time-dependent variable.

Journal of Physics Conference Series•Jun 10, 2013•8 citations

The Exact Solution, Berry's Phase and Coherent State for the Driven Generalized Time-Dependent Harmonic Oscillator

Jing‐Bo Xu, Tiezheng Qian, Xiao-Chun Gao

The Lewis' invariant and exact solution for the driven generalized time-dependent harmonic oscillator is found by making use of the Lewis-Riesenfeld quantum theory. Then, the adiabatic asymptotic limit of the exact solution is discussed and the Berry's phase for this system is obtained. We then proceed to use the exact solution to construct the coherent state and calculate the corresponding exact classical phase angle. This phase angle can give the Hannay's angle in the adjabatic limit. The relation between the exact Lewis' phase and the corresponding classical phase angle is discussed.

Communications in Theoretical Physics•Oct 1, 1991•0 citations

THE EXACT SOLUTION AND BERRY'S PHASE FOR THE GENERALIZED TIME-DEPENDENT HARMONIC OSCILLATOR

GAO XIAO-CHUN, XU JIN-BO, Tiezheng Qian +1 more

In this paper, we find the exact solution for the generalized time-dependent harmonic oscillator by making use of the Lewis-Riesenfeld theory. Then, the adiabatic asymptotic limit of the exact solution is discussed and the Berry's phase factor for the oscillator obtained. We proceed to use the exact solution to construct the coherent state and calculate the corresponding classical Hannay angle.

Acta Physica Sinica•Jan 1, 1991•1 citation

Generalized path-integral solution and coherent states of the harmonic oscillator in D -dimensions

Ma Yu-Quan, Jin Zhang, Chen Yong-Kang +1 more

We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time-dependent forced harmonic oscillator in D ( D ⩾ 1) dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D -dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.

Chinese Physics•Oct 31, 2005•1 citation
In this paper, the annihilation and creation operators are defined directly for the generalized time dependent harmonic oscillator. And the time dependent particle number representation is constructed, in which the adiabatic quantum phase is obtained, the adiabatic time dependent coherent states are found, and the essential properties for the coherent states are also discussed.
The dynamical invariant for a general time-dependent harmonic oscillator is constructed by making use of two linearly independent solutions to the classical equation of motion. In terms of this dynamical invariant we define the time-dependent creation and annihilation operators and relevantly introduce even and odd coherent states for time-dependent harmonic oscillator. The mathematical and quantum statistical properties of these states are discussed in detail. The harmonic oscillator with periodically varying frequency is treated as a demonstration of our general approach.
Based on Gaussian wave packet solutions of the time-dependent Schrödinger equation, a generalization of the conventional creation and annihilation operators and the corresponding coherent states can be obtained. This generalization includes systems where also the width of the coherent states is time-dependent as they occur for harmonic oscillators with time-dependent frequency or systems in contact with a dissipative environment. The key point is the replacement of the frequency ω 0 that occurs in the usual definition of the creation/annihilation operator by a complex time-dependent function that fulfils a nonlinear Riccati equation. This equation and its solutions depend on the system under consideration and on the (complex) initial conditions. Formal similarities also exist with supersymmetric quantum mechanics. The generalized creation and annihilation operators also allow to construct exact analytic solutions of the free motion Schrödinger equation in terms of Hermite polynomials with time-dependent variable.
The Lewis' invariant and exact solution for the driven generalized time-dependent harmonic oscillator is found by making use of the Lewis-Riesenfeld quantum theory. Then, the adiabatic asymptotic limit of the exact solution is discussed and the Berry's phase for this system is obtained. We then proceed to use the exact solution to construct the coherent state and calculate the corresponding exact classical phase angle. This phase angle can give the Hannay's angle in the adjabatic limit. The relation between the exact Lewis' phase and the corresponding classical phase angle is discussed.