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

American Journal of Physics

Coherent states and accidental degeneracy for a charged particle in a magnetic field

G. Loyola, M. Moshińsky, Adam P. Szczepaniak

Published Sep 1, 1989• 16 citations
Publisher

Abstract

The coherent state solution for a charged particle in a constant magnetic field and its implication for the accidental degeneracy present in the problem are discussed. Furthermore, a simple derivation is given for the density of electrons per unit area in the plane perpendicular to the magnetic field, which is required for the understanding of the quantum Hall effect.

DOI
10.1119/1.15898

Related papers

Detailed solution of the problem of Landau states in a symmetric gauge

Orion Ciftja

Abstract Understanding the quantum problem of a free charged particle undergoing two-dimensional motion in a perpendicular uniform, constant magnetic field is necessary to the comprehension of some very important phenomena in physics. In particular, a grasp of the nature of the Landau states in a symmetric gauge is crucial to explain the underlying principles of quantum Hall effects. In this work we provide a step-by-step solution of this quantum problem in a pedagogical fashion that is easy to follow by an audience of undergraduate students and prospective physics teachers. This approach should enable undergraduate students to comprehend all the technical mathematical details involved in the process. Such details are routinely missing from mainstream quantum mechanics textbooks. In particular, this study allows a broad audience of students and teachers to gradually absorb knowledge not only on basic principles of quantum mechanics, but also on various special mathematical functions that are encountered in the process.

European Journal of Physics•Feb 21, 2020•36 citations

Phase operator for a charged particle in a magnetic field

Shlomo Ruschin, J. Žák

A phase operator for a charged particle in a magnetic field is defined by using the classical connection between the angles in the configuration and the velocity planes (both perpendicular to the magnetic field). Coherent states are used for fixing the center of the orbit. The same states are also used in establishing quantization rules for classical functions containing products of quantities that do not commute in quantum mechanics.

Physical Review A•Sep 1, 1979•0 citations

Coherent states and dissipation for the motion of a charged particle in a constant magnetic field

Dieter Schuch, M. Moshińsky

We deal with the motion of a charged particle in a constant magnetic field when immersed in a medium that exerts some type of friction. We analyse the problem classically and also quantum mechanically. In the latter case we use coherent state solutions of the problem that, for large energies, compared with the one associated with the cyclotron frequency, reduce to the classical limit. To study the dynamical behaviour we use time-dependent wave packets that can be constructed by superposition of the coherent states.

Journal of Physics A Mathematical and General•May 28, 2003•23 citations

A charged particle in a magnetic field: a review of two formalisms of coherent states and the Husimi function

Dianela Herrera, Ana M. Valencia, F. Pennini +1 more

In this work, we review two formalisms of coherent states for the case of a particle in a magnetic field. We focus our revision on both pioneering (Feldman and Kahn 1970 Phys. Rev. B 1 4584) and recent (Kowalski and Rembieliński 2005 J. Phys. A: Math. Gen. 38 8247 ) formulations of coherent states for this problem. We introduce a general application, the Husimi function, which takes into account collective and environmental effects, and which can be derived in a variety of ways. However, we calculate this function as the expected value of the density operator in a basis of coherent states.

European Journal of Physics•Mar 5, 2008•5 citations

States of a Charged Particle with a Tensor-Like Mass in External Constant Magnetic Field

A.A. Borghardt, D.Ya. Karpenko, D.V. Kashkakha

Solutions of the Schrödinger equation for a particle with a tensor-like mass are considered. It is shown that the problem of determination of the coherent states in this case is reduced to integration of the nonlinear system of ordinary differential equations.

Journal of Nonlinear Mathematical Physics•Jan 1, 1997•0 citations

A solution (Dirac electron in crossed, constant electric and magnetic fields) that has found a problem (relativistic quantized Hall effect)

Michael Martin Nieto, Philip L. Taylor

The exactly solvable Dirac electron in crossed, constant electric and magnetic fields represents the relativistic quantized Hall effect. The solution allows one to show that there are no relativistic quantum-mechanical corrections to the ordinary quantized Hall effect.

American Journal of Physics•Mar 1, 1985•14 citations
The coherent state solution for a charged particle in a constant magnetic field and its implication for the accidental degeneracy present in the problem are discussed. Furthermore, a simple derivation is given for the density of electrons per unit area in the plane perpendicular to the magnetic field, which is required for the understanding of the quantum Hall effect.
Abstract Understanding the quantum problem of a free charged particle undergoing two-dimensional motion in a perpendicular uniform, constant magnetic field is necessary to the comprehension of some very important phenomena in physics. In particular, a grasp of the nature of the Landau states in a symmetric gauge is crucial to explain the underlying principles of quantum Hall effects. In this work we provide a step-by-step solution of this quantum problem in a pedagogical fashion that is easy to follow by an audience of undergraduate students and prospective physics teachers. This approach should enable undergraduate students to comprehend all the technical mathematical details involved in the process. Such details are routinely missing from mainstream quantum mechanics textbooks. In particular, this study allows a broad audience of students and teachers to gradually absorb knowledge not only on basic principles of quantum mechanics, but also on various special mathematical functions that are encountered in the process.
We deal with the motion of a charged particle in a constant magnetic field when immersed in a medium that exerts some type of friction. We analyse the problem classically and also quantum mechanically. In the latter case we use coherent state solutions of the problem that, for large energies, compared with the one associated with the cyclotron frequency, reduce to the classical limit. To study the dynamical behaviour we use time-dependent wave packets that can be constructed by superposition of the coherent states.
In this work, we review two formalisms of coherent states for the case of a particle in a magnetic field. We focus our revision on both pioneering (Feldman and Kahn 1970 Phys. Rev. B 1 4584) and recent (Kowalski and Rembieliński 2005 J. Phys. A: Math. Gen. 38 8247 ) formulations of coherent states for this problem. We introduce a general application, the Husimi function, which takes into account collective and environmental effects, and which can be derived in a variety of ways. However, we calculate this function as the expected value of the density operator in a basis of coherent states.