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

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Coherent states for the time-dependent harmonic oscillator

John G. Hartley, John R. Ray

Published Jan 15, 1982• 129 citations
Publisher

Abstract

Exact coherent states for the time-dependent harmonic oscillator are constructed. These new coherent states have most, but not all, of the properties of the coherent states for the time-independent oscillator. For example, these coherent states give the exact classical motion, but they are not minimum-uncertainty states.
DOI
10.1103/physrevd.25.382

Related papers

New coherent states with applications to time-dependent systems

A. K. Rajagopal, John T. Marshall

A new class of coherent states is defined, having all the properties of the usual coherent states except that the uncertainty product of position and momentum need not be minimum. From the stationary-action principle, the dynamical equations of motion for the expectation values and uncertainties for position and momentum are deduced. For the time-dependent harmonic oscillator, the equation for the uncertainty in the position is found to be the well-known Lewis constraint.

Physical Review A•Nov 1, 1982•60 citations

Quasi-coherent states for harmonic oscillator with time-dependent parameters

Nuri Ünal

In this study, we discuss the harmonic oscillator with the time-dependent frequency, ω(t), and the mass, M(t), by generalizing the holomorphic coordinates for the harmonic oscillator. In general cases, we solve the Schrödinger equation by reducing it into the Riccati equation and discuss the uncertainties for the quasi-coherent states of the time-dependent harmonic oscillator. In special cases, we find the following results: First, for a time-dependent harmonic oscillator, if [ω(t)M(t)] is constant, then the coherent states will evolve as the coherent states. Second, for the driven harmonic oscillator, the coherent states will evolve as the coherent states with new eigenvalues. Third, we derive quasi-coherent states for the Caldirola–Kanai Hamiltonian and show that the product of uncertainties, ΔxΔp, is larger than minimum value; however, it is constant. We also discuss the classical equations of motion for the system.

Journal of Mathematical Physics•Jan 1, 2012•13 citations

Exact wave functions and coherent states of a damped driven harmonic oscillator

H. G. Oh, H. R. Lee, Thomas F. George +1 more

For a damped harmonic oscillator forced by a time-dependent field, the exact wave function is obtained by three different methods: (i) path integral, (ii) second quantization, and (iii) dynamical invariant. The explicit form of the dynamical invariant involves a solution to a corresponding auxiliary equation. The coherent states, defined as eigenstates of a new destruction operator, form a nonorthogonal, overcomplete set and correspond to the minimum uncertainty states. These coherent states give the exact classical motion of the damped driven harmonic oscillator.

Physical Review A•Jun 1, 1989•40 citations

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

Coherent states for the damped harmonic oscillator

Kyu Hwang Yeon, Chung‐In Um, Thomas F. George

Using the Caldirola-Kanai Hamiltonian for the damped harmonic oscillator, exact coherent states are constructed. These new coherent states satisfy the properties which coherent states should generally have.

Physical Review A•Dec 1, 1987•81 citations

Coherent states for the cranked harmonic oscillator

Mohammed A. Z. Habeeb

Exact coherent states for a particle moving in a cranked anisotropic harmonic oscillator potential are constructed and their properties investigated. It is found that although these states are not minimum-uncertainty states they give the exact classical motion. As an application, it is shown that these coherent states can be used to facilitate the derivation, in the semi-classical limit, of the equations of fluid dynamics in a rotating frame corresponding to a nucleon in a rotating nucleus.

Journal of Physics G Nuclear Physics•May 1, 1987•6 citations
In this study, we discuss the harmonic oscillator with the time-dependent frequency, ω(t), and the mass, M(t), by generalizing the holomorphic coordinates for the harmonic oscillator. In general cases, we solve the Schrödinger equation by reducing it into the Riccati equation and discuss the uncertainties for the quasi-coherent states of the time-dependent harmonic oscillator. In special cases, we find the following results: First, for a time-dependent harmonic oscillator, if [ω(t)M(t)] is constant, then the coherent states will evolve as the coherent states. Second, for the driven harmonic oscillator, the coherent states will evolve as the coherent states with new eigenvalues. Third, we derive quasi-coherent states for the Caldirola–Kanai Hamiltonian and show that the product of uncertainties, ΔxΔp, is larger than minimum value; however, it is constant. We also discuss the classical equations of motion for the system.
For a damped harmonic oscillator forced by a time-dependent field, the exact wave function is obtained by three different methods: (i) path integral, (ii) second quantization, and (iii) dynamical invariant. The explicit form of the dynamical invariant involves a solution to a corresponding auxiliary equation. The coherent states, defined as eigenstates of a new destruction operator, form a nonorthogonal, overcomplete set and correspond to the minimum uncertainty states. These coherent states give the exact classical motion of the damped driven harmonic oscillator.
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.