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 Physics A Mathematical and General

On the propagator of a charged particle in a constant magnetic field and with a quadratic potential

Bin Kang Cheng

Published Mar 11, 1984• 25 citations
Publisher

Abstract

The author shows that the propagator of a charged particle in a constant external magnetic field and with a quadratic potential is related to the propagator of a one-dimensional time-dependent forced harmonic oscillator with generalised memory. For special cases, the author evaluates the propagator exactly with the help of a gaussian integral. Results are in agreement with well known results for simple cases.

DOI
10.1088/0305-4470/17/4/022

Related papers

Exact Evaluation of the Propagator for a Charged Particle in a Constant Magnetic Field

Bin Kang Cheng

We are able to show that the propagator for a charged particle in a constant external magnetic field is related to that of a one-dimensional forced harmonic oscillator with memory, which can then be easily evaluated with the help of a gaussian integral.

Physica Scripta•Apr 1, 1984•7 citations

Exact evaluation of the propagator beyond and at caustics for a charged particle in a constant magnetic field

Bin Kang Cheng

It is first shown that the propagator of a charged particle in a constant external magnetic field is related to the propagator of a one-dimensional driven harmonic oscillator with memory. The memory term can be removed by introducing the auxiliary force term and then by integrating it out. By using this new formula for a driven harmonic oscillator, a generalization of Horv\'athy-Feynman formula, we finally evaluate exactly the propagator beyond and at caustics of our dynamical system.

Physical Review A•Sep 1, 1984•5 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 anisotropic oscillator in a constant magnetic field

N. Kokiantonis, K Castrigiano

The propagator for a charged, anisotropic harmonic oscillator in a constant magnetic field is computed. Making use of this an explicit expression is given for the path integral to an action with generalised memory recently considered in the literature.

Journal of Physics A Mathematical and General•Jan 11, 1985•20 citations

Exact Propagator of a Two Dimensional Anisotropic Harmonic Oscillator in the Presence of a Magnetic Field

José M. Cerveró

In this paper we solve exactly the problem of the spectrum and Feynman propagator of a charged particle submitted to both an anharmonic oscillator in the plane and a constant and homogeneous magnetic field of arbitrary strength aligned with the perpendicular direction to the plane. As we shall see in the beginning of the letter, the Hamiltonian, being a quadratic form, is easily diagonalizable and the Classical Action can be used to construct the exact Feynman Propagator using the Stationary Phase Approximation. The result is useful for the treatment of quasi two dimensional samples in the field of magnetic effects in nano-structures and quantum optics. The presented solution, after minor extensions, can also be used for motion in three dimensions, and in fact it has been used for years in such cases. Also it can be used as a good exercise of a Feynman Path Integral that can be calculated easily with just the help of the Classical Action.

arXiv:1611.05217•Journal of Modern Physics•Jan 1, 2017•1 citation

Fock Bargmann space and Feynman propagator of charged harmonic oscillator in a constant magnetic field.

Mehdi Hage-Hassan

The Feynman propagator of charged harmonic oscillator in a constant magnetic field is found for the first time by a direct calculation using Fock Bargmann space and a new generating function of two dimensional harmonic oscillators. The calculations involve well-known integrals which an undergraduate should understand.

•Aug 27, 2010•0 citations
The author shows that the propagator of a charged particle in a constant external magnetic field and with a quadratic potential is related to the propagator of a one-dimensional time-dependent forced harmonic oscillator with generalised memory. For special cases, the author evaluates the propagator exactly with the help of a gaussian integral. Results are in agreement with well known results for simple cases.
In this paper we solve exactly the problem of the spectrum and Feynman propagator of a charged particle submitted to both an anharmonic oscillator in the plane and a constant and homogeneous magnetic field of arbitrary strength aligned with the perpendicular direction to the plane. As we shall see in the beginning of the letter, the Hamiltonian, being a quadratic form, is easily diagonalizable and the Classical Action can be used to construct the exact Feynman Propagator using the Stationary Phase Approximation. The result is useful for the treatment of quasi two dimensional samples in the field of magnetic effects in nano-structures and quantum optics. The presented solution, after minor extensions, can also be used for motion in three dimensions, and in fact it has been used for years in such cases. Also it can be used as a good exercise of a Feynman Path Integral that can be calculated easily with just the help of the Classical Action.