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

International Journal of Modern Physics E

A REALIZATION OF DYNAMIC GROUP FOR AN ELECTRON IN A UNIFORM MAGNETIC FIELD

Shishan Dong, Shi‐Hai Dong

Published Aug 1, 2002• 14 citations
Publisher

Abstract

The eigenvalues and eigenfunctions of the Schrödinger equation with a non-relativistic electron in a uniform magnetic field are presented. A realization of the creation and annihilation operators for the radial wave-functions is carried out. It is shown that these operators satisfy the commutation relations of an SU(1,1) group. Closed analytical expressions are evaluated for the matrix elements of different functions ρ2 and [Formula: see text].

DOI
10.1142/s0218301302000831

Related papers

An algebraic approach for a charged particle in a certain magnetic field

Mohammad Reza Setare, Ghafar Olfati

The properties of the charged particle in a certain varying magnetic field are outlined. A realization of the creation and annihilation operators for the wavefunctions is studied. It is shown that these operators satisfy the commutation relation of an SU(1,1) group. The closed analytical expressions for the matrix elements of different function ρ and ρ(d/dρ) are evaluated.

Physica Scripta•Jan 25, 2007•12 citations

On some Properties of the Schrauben Functions in Connection with the Magnetic Operators

A. D. Jannussis, P. Tsilimigras

Abstract In this paper we introduce two new "magnetic" operators and we show that these are the creation and annihilation operators of the schrauben functions. The schrauben functions are the eigenfunctions of the Hamilton operator describing a free electron under the action of a uniform magnetic field. By transforming these two operators we obtain two other operators which we show to be of Harpers type, as was expected.

Zeitschrift für Naturforschung A•Mar 1, 1969•3 citations

THE HIDDEN SYMMETRY FOR A QUANTUM SYSTEM WITH A PÖSCHL–TELLER-LIKE POTENTIAL

Shi‐Hai Dong, Guo-Hua Sun, Yu Tang

The eigenvalues and eigenfunctions of the Schrödinger equation with a Pöschl–Teller (PT)-like potential are presented. A realization of the creation and annihilation operators for the wave functions is carried out. It is shown that these operators satisfy the commutation relations of an SU(1,1) group. Closed analytical expressions are evaluated for the matrix elements of different functions, sin (ρ) and [Formula: see text] with ρ=πx/L.

International Journal of Modern Physics E•Dec 1, 2003•21 citations

Motion in a Constant Magnetic Field

M. H. Johnson, Bernard A. Lippmann

The motion of a charged particle in a constant magnetic field is treated in both relativistic and non-relativistic quantum theory. Operators representing the center of the orbit, which obey the commutation law for conjugate variables, are introduced and their connections with energy, angular momentum, and magnetic moment studied. Energy eigenfunctions in an operator form are obtained by factorization. Previously derived eigenfunctions in coordinate space are obtained and are shown to be eigenfunctions for the operators for the center of the orbit as well as for the energy. Corresponding relativistic eigenfunctions are derived by a simple device which enables one to construct solutions of the Dirac equation from solutions of the Schr\"odinger equation.

Physical Review•Sep 15, 1949•451 citations

An Algebraic Approach to the Harmonic Oscillator Plus an Inverse Square Potential in Three Dimensions

Shi‐Hai Dong, M. Lozada-Cas

The eigenfunctions and eigenvalues of the three-dimensional Schrödinger equation with a harmonic oscillator plus an inverse square interaction are obtained. A realization of the ladder operators for the wave functions is studied. It is found that these operators satisfy the commutation relations of an SU(1,1) group. The closed analytical expressions for the matrix elements of different functions ρ and ρd/dρ with ρ = r 2 are evaluated. Another hidden symmetry explores the relations between the eigenvalues and eigenfunctions for substituting r→ ir. PACS number(s): 03. 65. Fd, 03. 65.Ge and 02. 20.Qs.

American Journal of Applied Sciences•Jan 1, 2005•11 citations

Paraxial wave function and Gouy phase for a relativistic electron in a uniform magnetic field

Liping Zou, Pengming Zhang, Alexander J Silenko

Abstract A connection between relativistic quantum mechanics in the Foldy–Wouthuysen representation and the paraxial equations is established for a Dirac particle in external fields. The paraxial form of the Landau eigenfunction for a relativistic electron in a uniform magnetic field is determined. The obtained wave function contains the Gouy phase and significantly approaches the paraxial wave function for a free electron.

arXiv:2003.04717•Journal of Physics G Nuclear and Particle Physics•Feb 28, 2020•12 citations
The eigenvalues and eigenfunctions of the Schrödinger equation with a non-relativistic electron in a uniform magnetic field are presented. A realization of the creation and annihilation operators for the radial wave-functions is carried out. It is shown that these operators satisfy the commutation relations of an SU(1,1) group. Closed analytical expressions are evaluated for the matrix elements of different functions ρ2 and [Formula: see text].
The motion of a charged particle in a constant magnetic field is treated in both relativistic and non-relativistic quantum theory. Operators representing the center of the orbit, which obey the commutation law for conjugate variables, are introduced and their connections with energy, angular momentum, and magnetic moment studied. Energy eigenfunctions in an operator form are obtained by factorization. Previously derived eigenfunctions in coordinate space are obtained and are shown to be eigenfunctions for the operators for the center of the orbit as well as for the energy. Corresponding relativistic eigenfunctions are derived by a simple device which enables one to construct solutions of the Dirac equation from solutions of the Schr\"odinger equation.
The eigenfunctions and eigenvalues of the three-dimensional Schrödinger equation with a harmonic oscillator plus an inverse square interaction are obtained. A realization of the ladder operators for the wave functions is studied. It is found that these operators satisfy the commutation relations of an SU(1,1) group. The closed analytical expressions for the matrix elements of different functions ρ and ρd/dρ with ρ = r 2 are evaluated. Another hidden symmetry explores the relations between the eigenvalues and eigenfunctions for substituting r→ ir. PACS number(s): 03. 65. Fd, 03. 65.Ge and 02. 20.Qs.