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

Communications in Theoretical Physics

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

Published Sep 15, 1994• 0 citations
Publisher

Abstract

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.
DOI
10.1088/0253-6102/22/2/135

Related papers

Path integral solution to a charged particle in an infinite square-well potential with a constant electric field

Kyu Hwang Yeon, Chung‐In Um, Thomas F. George +1 more

The propagator of a charged particle in an infinite square-well potential in one dimension with a constant electric field is solved exactly using Feynman path integration. The wave function of the system is evaluated by the propagator. This wave function depends on time in a way determined by the well size, particle mass and charge, and applied electric field. The uncertainty relation of the system is also obtained by this function.

Canadian Journal of Physics•Sep 1, 1994•2 citations

Propagator for the time-dependent three-dimensional charged harmonic oscillator in a time-varying magnetic field

Antnio B. Nassar, Ruth T. Berg

We evaluate the exact propagator for the time-dependent three-dimensional charged harmonic oscillator in a time-varying magnetic field. We show that such a propagator can be obtained from that for a charged particle in a constant magnetic field.

Physical Review A•Sep 1, 1986•20 citations

Propagator for a Charged Particle in Time-Dependent Electromagnetic Field and Quadratic Potential

Bin Kan Cheng

Through a t ime-dependent l inear transformation a nd the time substitution, we can evaluate exactly the propagator for a charged par- ticle in a time-dependent electromagnetic f ield subjected to a time- -dependent quadratic potential.

•Jan 1, 1987•0 citations

A path-integral approach to expectation values in time-dependent problems

J. Poulter

Within the framework of Feynman path integration, expectation values of quantum mechanical operators may be exactly obtained for a class of time-dependent problems. Attention is focused on the two-dimensional motion of a charged particle in a perpendicular magnetic field with a time-dependent driving force. A harmonic oscillator potential is included to ensure that the corresponding density matrix is properly defined although some expectation values are defined without it. This potential is at least a mathematical convenience. Some discussion concerning the conditions under which steady states may be attained is also included.

Journal of Physics A Mathematical and General•Jul 7, 1994•1 citation

Charged Particle in a Time-dependent Electric Field: A White Noise Functional Approach

E. B. Gravador, Jinky B. Bornales, M. J. Liwanag +2 more

The propagator for a charged particle in a time‐dependent electric field is calculated following Hida and Streit's framework [1] where the propagator is the T‐transform of Feynman functional. However, we have to regard the potential V = −qE(τ)x≡mℏξ̇x following C. C. Bernido and M. V. Carpio‐Bernido's [2] prescription of time‐dependent potentials. The result agrees with the limiting form of Eqn. (16) of N. Morgenstern Horing, H. L. Cui, and G. Fiorenza [3], when the magnetic field is switched off, and Eqn. (17) of [3] when the electric field is constant in time.

AIP conference proceedings•Jan 1, 2008•0 citations

Unitary transformation technique for the study of quantum dynamics of charged particle in time-dependent electromagnetic field

Rachid Ahmim, Nabil Baouche, Askri Souhaila +2 more

In this paper, we present a unitary transformation technique to solve the equation of quantum dynamics of a charged particle moving in a time-dependent electromagnetic field. The primary advantage of the technique lies in the connection of this technique with one of the essential features of the system which is the gauge. The gauge has been chosen in a way where the first three dimensional Hamiltonian transformed easily through this technique to a two dimensional coupled problem. This problem is central in several areas of physics, including solid-state and plasma physics, where the understanding of the behavior of charged particles in the presence of time-dependent electromagnetic fields is essential to explore the behavior of various phenomena. The complete solution of the Schrödinger equation is presented and the propagator is also determined using this technique. This technique is also used to shows how the problem can be reduced to a two-dimensional system of coupled harmonic oscillators, each subjected to a time-dependent linear potential. This reduction simplifies the analysis by transforming the problem into a form that can be mapped onto a well-established model, which has been previously studied using the path integral formalism.

STUDIES IN ENGINEERING AND EXACT SCIENCES•Dec 13, 2024•0 citations
Within the framework of Feynman path integration, expectation values of quantum mechanical operators may be exactly obtained for a class of time-dependent problems. Attention is focused on the two-dimensional motion of a charged particle in a perpendicular magnetic field with a time-dependent driving force. A harmonic oscillator potential is included to ensure that the corresponding density matrix is properly defined although some expectation values are defined without it. This potential is at least a mathematical convenience. Some discussion concerning the conditions under which steady states may be attained is also included.
The propagator for a charged particle in a time‐dependent electric field is calculated following Hida and Streit's framework [1] where the propagator is the T‐transform of Feynman functional. However, we have to regard the potential V = −qE(τ)x≡mℏξ̇x following C. C. Bernido and M. V. Carpio‐Bernido's [2] prescription of time‐dependent potentials. The result agrees with the limiting form of Eqn. (16) of N. Morgenstern Horing, H. L. Cui, and G. Fiorenza [3], when the magnetic field is switched off, and Eqn. (17) of [3] when the electric field is constant in time.
In this paper, we present a unitary transformation technique to solve the equation of quantum dynamics of a charged particle moving in a time-dependent electromagnetic field. The primary advantage of the technique lies in the connection of this technique with one of the essential features of the system which is the gauge. The gauge has been chosen in a way where the first three dimensional Hamiltonian transformed easily through this technique to a two dimensional coupled problem. This problem is central in several areas of physics, including solid-state and plasma physics, where the understanding of the behavior of charged particles in the presence of time-dependent electromagnetic fields is essential to explore the behavior of various phenomena. The complete solution of the Schrödinger equation is presented and the propagator is also determined using this technique. This technique is also used to shows how the problem can be reduced to a two-dimensional system of coupled harmonic oscillators, each subjected to a time-dependent linear potential. This reduction simplifies the analysis by transforming the problem into a form that can be mapped onto a well-established model, which has been previously studied using the path integral formalism.