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

Annals of Physics

Propagator for the time-dependent charged oscillator via linear and quadratic invariants

M. Sebawe Abdalla, Jeong-Ryeol Choi

Published Jan 22, 2007• 37 citations
Publisher
DOI
10.1016/j.aop.2007.01.006

Related papers

Quadratic invariants and coherent states of a general time-dependent harmonic oscillator

S. N. Pandey, U. B. Dubey

Pramana•Jan 1, 1992•0 citations

The propagator for a charged oscillator with a time-dependent mass in a time-varying electromagnetic field

ALVARO DE SOUZA DUTRA, Carlos Farina de Souza, Luiz Claudio M. de Albuquerque

Physics Letters A•Jul 1, 1991•21 citations

Propagators for time-dependent linear and quadratic potentials and inverse Weierstrass transform

B. Bassetti, E. Montaldi, Mario Raciti

Physics Letters A•Jul 1, 1982•2 citations

Propagator for the general time-dependent harmonic oscillator with application to an ion trap

Gal Harari, Y. Ben-Aryeh, A. Mann

We present the simplest possible formula for the propagator of the general time-dependent quadratic Hamiltonian, including linear terms. The method is based on the use of a linear time-dependent invariant and requires only the solution of a linear homogeneous second-order ordinary differential equation corresponding to the classical quadratic Hamiltonian. We give an example for the case of the Paul trap.

Physical Review A•Dec 2, 2011•27 citations

Propagator for a charged particle in a time-dependent electromagnetic field

Bin Kang Cheng

Physics Letters A•Feb 1, 1984•4 citations

On the quantization of the electromagnetic field in conducting media

Alberes Lopes de Lima, Alexandre Rosas, I. A. Pedrosa

In this work we investigate the quantization of electromagnetic waves propagating through homogeneous conducting linear media with no charge density. We use Coulomb's gauge to reduce the problem to that of a time-dependent harmonic oscillator, which is described by the Caldirola–Kanai Hamiltonian. Furthermore, we obtain the corresponding exact wave functions with the help of quadratic invariants and of the dynamic invariant method. These wave functions are written in terms of a particular solution of the Milne–Pinney equation. We also construct coherent and squeezed states for the quantized electromagnetic waves and evaluate the quantum fluctuations in coordinates and momentum as well as the uncertainty product for each mode of the electromagnetic field.

Journal of Modern Optics•Dec 17, 2008•7 citations
In this work we investigate the quantization of electromagnetic waves propagating through homogeneous conducting linear media with no charge density. We use Coulomb's gauge to reduce the problem to that of a time-dependent harmonic oscillator, which is described by the Caldirola–Kanai Hamiltonian. Furthermore, we obtain the corresponding exact wave functions with the help of quadratic invariants and of the dynamic invariant method. These wave functions are written in terms of a particular solution of the Milne–Pinney equation. We also construct coherent and squeezed states for the quantized electromagnetic waves and evaluate the quantum fluctuations in coordinates and momentum as well as the uncertainty product for each mode of the electromagnetic field.