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 Mathematical Physics

Path integral for the damped harmonic oscillator coupled to its dual

L. Chétouani, Larbi Guechi, Théophile F. Hammann, M. Letlout

Published Mar 1, 1994• 4 citations
Publisher

Abstract

The time independent Bateman model which describes the damped harmonic oscillator coupled to its dual is studied using the path integral approach. The related propagator is calculated by means of the matrix representation.
DOI
10.1063/1.530634

Related papers

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

Quantum mechanics of the damped harmonic oscillator

Massimo Blasone A, Petr Jizba B

We quantize the system of a damped harmonic oscillator coupled to its time-reversed image, known as Bateman's dual system. By using the Feynman–Hibbs method, the time-dependent quantum states of such a system are constructed entirely in the framework of the classical theory. The geometric phase is calculated and found to be proportional to the ground-state energy of the one-dimensional linear harmonic oscillator to which the two-dimensional system reduces under appropriate constraint. PACS Nos.: 03.65Ta, 03.65Vf, 03.65Ca, 03.65Fd

Canadian Journal of Physics•Jun 1, 2002•25 citations

On the quantum mechanics of dissipative Lagrangians

G J Papadopoulos

An appropriate path differential measure is employed for obtaining the path integral representation of the propagator of a particle with a time dependent 'mass'. The evaluations are restricted to quadratic Lagrangians and the propagator for the damped harmonic oscillator is given explicitly.

Journal of Physics A Mathematical Nuclear and General•Jan 21, 1974•16 citations

Propagators for a particle in a time-dependent linear potential and a free particle

Surarit Pepore, R Biswas

In this paper, the propagators for a particle moving in a time-dependent linear potential and a free particle with linear damping are calculated by the application of the integrals of the motion of a quantum system. The propagator for a charged harmonic oscillator is derived from the Feynman path integrals and the propagator for a damped harmonic oscillator is evaluated by the Schwinger method. The relation between the integrals of the motion, Feynman path integrals, and Schwinger method are also described.

Physics & Astronomy International Journal•Oct 19, 2021•1 citation

Exact evaluation of the propagator for the damped harmonic oscillator

Bin Kang Cheng

Using the Caldirola-Kanai Hamiltonian for the quantum dissipative system, the author expresses the propagator as the modified Feynman path integral in the configuration space, which can then be evaluated for the damped harmonic oscillator by Montroll's method. The propagator of the damped harmonic oscillator can also be calculated beyond and at caustics with the help of Horvathy-Feynman formula. The new results are confirmed by investigating the classical paths joining two fixed end-point positions, Finally the author obtains the time-dependent wavefunctions from the propagator of the dynamical system.

Journal of Physics A Mathematical and General•Aug 21, 1984•14 citations

PROPAGATOR AND EXACT WAVE FUNCTION OF THE TIME DEPENDENTLY DAMPED HARMONIC OSCILLATOR

Ling Rui-liang, 常熟高等专科学校物理系,常熟215500

By means of canonical transformation,a direct quantization scheme is found for a harmonic oscillator whose damping coefficient is time-dependent.By adopting the Gaussian-type propagator and Feynman's path integral method,the exact wave function is derived.Some discussions made.

Acta Physica Sinica•Jan 1, 2001•1 citation
We quantize the system of a damped harmonic oscillator coupled to its time-reversed image, known as Bateman's dual system. By using the Feynman–Hibbs method, the time-dependent quantum states of such a system are constructed entirely in the framework of the classical theory. The geometric phase is calculated and found to be proportional to the ground-state energy of the one-dimensional linear harmonic oscillator to which the two-dimensional system reduces under appropriate constraint. PACS Nos.: 03.65Ta, 03.65Vf, 03.65Ca, 03.65Fd
In this paper, the propagators for a particle moving in a time-dependent linear potential and a free particle with linear damping are calculated by the application of the integrals of the motion of a quantum system. The propagator for a charged harmonic oscillator is derived from the Feynman path integrals and the propagator for a damped harmonic oscillator is evaluated by the Schwinger method. The relation between the integrals of the motion, Feynman path integrals, and Schwinger method are also described.
Using the Caldirola-Kanai Hamiltonian for the quantum dissipative system, the author expresses the propagator as the modified Feynman path integral in the configuration space, which can then be evaluated for the damped harmonic oscillator by Montroll's method. The propagator of the damped harmonic oscillator can also be calculated beyond and at caustics with the help of Horvathy-Feynman formula. The new results are confirmed by investigating the classical paths joining two fixed end-point positions, Finally the author obtains the time-dependent wavefunctions from the propagator of the dynamical system.