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

Canadian Journal of Physics

Path integral approach to the time-dependent quadratic Hamiltonian and coherent states

Jing‐Bo Xu, Ji-Ming Bao, Xiao-Chun Gao

Published Aug 1, 1992• 1 citation
Publisher

Abstract

The exact propagator and invariant for the time-dependent quadratic Hamiltonian is found by a generalized canonical transformation and a path integral method. We then proceed to construct the coherent states for the system by making use of the propagator. The coherent states for the damped harmonic oscillator and variable mass or frequency harmonic oscillator are the special cases of the coherent states for the system studied in this paper.

DOI
10.1139/p92-102

Related papers

Path integral approach to the general driven time-dependent harmonic oscillator and squeezed state

Jing‐Bo Xu, ZHANG XUN-SHENG, Shangbin Li

The time evolution of the general driven time-dependent harmonic oscillator is studied and the propagator and wave function are obtained by using a generalized canonical transformation and path integral method. We then proceed to construct the squeezed states for the system by making use of the wave function. The damped driven harmonic oscillator and the harmonic oscillator with strongly pulsating mass under the action of an arbitrary driving force are discussed as illustrative examples.

Physica Scripta•Sep 1, 1997•3 citations

Path integral for new models of time-dependent harmonic oscillators

Badri Berrabah, Baya Bentag

We have presented a particular direct method to solve time-dependent quantum problems within the framework of path integrals by using explicitly time-dependent transformations. We have applied it to the case of harmonic oscillator with time-dependent mass and frequency. Some examples have illustrated the method used. From their exact propagators, normalized solutions have been obtained.

International Journal of Geometric Methods in Modern Physics•Dec 12, 2019•1 citation

Quantum Mechanical Path Integral in Phase Space and Class of Harmonic Oscillators with Varied Frequencies

Badri Berrabah

We present the problem of the time-dependent Harmonic oscillator with time-dependent mass and frequency in phase space and by using a canonical transformation and delta functional integration we could find the propagator related to the system. New examples of time-dependent frequencies are presented.

Journal of Modern Physics•Jan 1, 2016•2 citations

Harmonic Oscillator, Coherent States, and Feynman Path Integral yz

Dae-Yup Song

The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to nd a complete set of wave functions for the oscillator. Harmonic oscillators with dierent (time-dependent) parameters can be related through unitary transformations. The existence of generalized coherent states for a simple harmonic oscillator can then be interpreted as the result of a (formal) invariance under a unitary transformation which relates the same harmonic oscillator. In the path integral formalism, the invariance is reflected in that the kernels do not depend on the choice of classical solutions.

•Nov 18, 2002•0 citations

Harmonic Oscillator, Coherent States, and Feynman Path Integral

Dae-Yup Song

The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to find a complete set of wave functions for the oscillator. Harmonic oscillators with different (time-dependent) parameters can be related through unitary transformations. The existence of generalized coherent states for a simple harmonic oscillator can then be interpreted as the result of a (formal) {\em invariance} under a unitary transformation which relates the same harmonic oscillator. In the path integral formalism, the invariance is reflected in that the kernels do not depend on the choice of classical solutions.

arXiv:quant-ph/0211106•Nov 18, 2002•1 citation

On the path integral quantization of the damped harmonic oscillator

Christopher C. Gerry

A time-dependent canonical transformation is performed in the path integral expression of the propagator for a damped harmonic oscillator to reduce it to a harmonic oscillator with modified frequency. The transformation is carried out in a properly time-symmetrized expression of the lattice space path integral by making expansions about the midpoint of each time interval.

Journal of Mathematical Physics•Jun 1, 1984•17 citations
The exact propagator and invariant for the time-dependent quadratic Hamiltonian is found by a generalized canonical transformation and a path integral method. We then proceed to construct the coherent states for the system by making use of the propagator. The coherent states for the damped harmonic oscillator and variable mass or frequency harmonic oscillator are the special cases of the coherent states for the system studied in this paper.
The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to nd a complete set of wave functions for the oscillator. Harmonic oscillators with dierent (time-dependent) parameters can be related through unitary transformations. The existence of generalized coherent states for a simple harmonic oscillator can then be interpreted as the result of a (formal) invariance under a unitary transformation which relates the same harmonic oscillator. In the path integral formalism, the invariance is reflected in that the kernels do not depend on the choice of classical solutions.
The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to find a complete set of wave functions for the oscillator. Harmonic oscillators with different (time-dependent) parameters can be related through unitary transformations. The existence of generalized coherent states for a simple harmonic oscillator can then be interpreted as the result of a (formal) {\em invariance} under a unitary transformation which relates the same harmonic oscillator. In the path integral formalism, the invariance is reflected in that the kernels do not depend on the choice of classical solutions.