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

Physica Scripta

Dynamics of a rotating particle under a time-dependent potential: exact quantum solution from the classical action

D. Laroze, Gonzalo Gutiérrez, Rodrigo Rivera, Julio M. Yáñez

Published Jul 1, 2008• 6 citations
Publisher

Abstract

The classical action for a three-dimensional rotating particle with time-dependent angular \nvelocity and that submitted to a general linear and quadratic time-dependent potential is \nexplicitly calculated and, via path integral approach, the quantum propagator is obtained. For \nsome special values of the coefficients, it is also shown that the quantum propagator in the \nrotating frame contains a phase factor which gives rise to a quantum interference phenomenon.

DOI
10.1088/0031-8949/78/01/015009

Related papers

Feynman propagator for time-dependent Lagrangians possessing an invariant quadratic in momentum

Asish Kumar Dhara, S. V. Lawande

A class of time-dependent classical Lagrangians possessing an invariant quadratic in momentum is considered from a quantal point of view. Quantum mechanics is introduced through the Feynman propagator defined as a path integral involving the classical action. It is shown, without carrying out an explicit path integration, that the propagator for such a time-dependent system is related to the propagator of an associated time-independent problem. The expansion of the propagator in terms of the eigenfunctions of the invariant operator is derived and the equivalence of the present theory to that of Lewis and Reisenfeld (1969) is discussed. Explicit analytic forms of propagators are obtained for some cases to illustrate the application of the present approach.

Journal of Physics A Mathematical and General•Aug 21, 1984•42 citations

Exact quantum theory of a time-dependent bound quadratic Hamiltonian system

Kyu Hwang Yeon, Kang Ku Lee, Chung‐In Um +2 more

Using the path-integral method, the propagator, the wave function, and the expectation values are evaluated explicitly for a time-dependent bound quadratic Hamiltonian system. We also have derived the relation between the wave function and a dynamical invariant which determines whether or not the system is bound. The expectation value of the quantum-mechanical invariant obeys the uncertainty relation with an auxiliary condition as the solution of the classical equation of the system.

Physical Review A•Oct 1, 1993•78 citations

Path Integral Approach to the Propagator for a Charged Particle in a Time-Dependent Electromagnetic Field

Jing‐Bo Xu, Yu-jun ZHAO, Xiao-Chun Gao

A path integral method is used to study the time evolution of a three-dimensional time-dependent system. The propagator for a charged particle in a time-dependent magnetic field and quadrupolar electric potential is obtained.

Communications in Theoretical Physics•Sep 15, 1994•0 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

Time-dependent general quantum quadratic Hamiltonian system

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

Solutions of the Schr\"odinger equation and propagators for the general quadratic and the linear Hamiltonian system of canonical variables whose coefficients are arbitrary and time dependent are obtained when the corresponding classical solution is oscillatory, linear, or monotonic. All of them are given by the coefficients of the Hamiltonian and the classical solution of the system under the conditions for which the classical solution exists.

Physical Review A•Nov 21, 2003•33 citations

On the exactness of the semi-classical approximation for non-relativistic one-dimensional propagators

I Semiz, K Düztaş

For one-dimensional non-relativistic quantum mechanical problems, we investigate the conditions for all the position dependence of the propagator to be in its phase, that is, for the semi-classical approximation to be exact. For velocity-independent potentials we find that: (i) the potential must be quadratic in space, but can have arbitrary time dependence, (ii) the phase may be made proportional to the classical action, and the magnitude (‘fluctuation factor’) can also be found from the classical solution and (iii) for the driven harmonic oscillator the fluctuation factor is independent of the driving term.

arXiv:quant-ph/0608211•Journal of Physics A Mathematical and General•Nov 8, 2006•0 citations
The classical action for a three-dimensional rotating particle with time-dependent angular \nvelocity and that submitted to a general linear and quadratic time-dependent potential is \nexplicitly calculated and, via path integral approach, the quantum propagator is obtained. For \nsome special values of the coefficients, it is also shown that the quantum propagator in the \nrotating frame contains a phase factor which gives rise to a quantum interference phenomenon.
A class of time-dependent classical Lagrangians possessing an invariant quadratic in momentum is considered from a quantal point of view. Quantum mechanics is introduced through the Feynman propagator defined as a path integral involving the classical action. It is shown, without carrying out an explicit path integration, that the propagator for such a time-dependent system is related to the propagator of an associated time-independent problem. The expansion of the propagator in terms of the eigenfunctions of the invariant operator is derived and the equivalence of the present theory to that of Lewis and Reisenfeld (1969) is discussed. Explicit analytic forms of propagators are obtained for some cases to illustrate the application of the present approach.
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.
For one-dimensional non-relativistic quantum mechanical problems, we investigate the conditions for all the position dependence of the propagator to be in its phase, that is, for the semi-classical approximation to be exact. For velocity-independent potentials we find that: (i) the potential must be quadratic in space, but can have arbitrary time dependence, (ii) the phase may be made proportional to the classical action, and the magnitude (‘fluctuation factor’) can also be found from the classical solution and (iii) for the driven harmonic oscillator the fluctuation factor is independent of the driving term.