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

RECEN - Revista Ciências Exatas e Naturais

Free-particle and harmonic-oscillator propagators in two and three dimensions

U Fernando Chaos, Lorea Chaos‐Cador, E. Ley‐Koo

Published Dec 14, 2009• 1 citation
OpenAlex

Abstract

This contribution illustrates how to construct free-particle and harmonic-oscillator quantum-mechanical propagators in two and three dimensions in cartesian, and in circular and spherical coordinates, respectively, starting from the corresponding one-dimensional propagators in cartesian coordinates.

Related papers

Common generating functions of complete harmonic oscillator wave functions and transformation brackets in D dimensions

Lorea Chaos‐Cador, E. Ley‐Koo

Abstract The separability of the Schrödinger equation for harmonic oscillators in D dimensions and in different coordinate systems (Cartesian, circular, spherical) makes possible the construction of common generating functions for the complete harmonic oscillator wave functions in the corresponding dimensions and coordinates. Explicit forms of such generating functions and their series expansions are presented, and one of their applications is illustrated through the evaluation of transformation brackets. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

International Journal of Quantum Chemistry•Nov 6, 2003•19 citations

Equivalence of the propagator of quasistatical solutions and the quantum harmonic oscillator

Cezar Augusto Bonato, M. T. Thomaz, Adolfo P. C. Malbouisson

We establish a connection between a two-dimensional field theory using a classical solution which depends only on one of the coordinates, and the quantum-mechanical harmonic oscillator whose frequency is one-coordinate dependent.

Physical Review A•Feb 1, 1989•4 citations

Relating the free particle with the harmonic oscillator

G. F. Torres del Castillo

We show that by means of a coordinate transformation in the extended configuration space the problem of a free particle can be related to that of a harmonic oscillator in classical mechanics and in quantum mechanics.

Revista Mexicana de Física•May 1, 2025•1 citation

The Feynman propagator within three parameters generalized Dunkl derivative: One-dimensional case

H. Benzair, Tahar Boudjedaa, M. Merad

In this paper, the Feynman path integral approach within three parameters Dunkl derivative is investigated in the one-dimensional case of nonrelativistic quantum mechanics. We successfully derive the propagator in Cartesian coordinates and give its exact expression for the free particle, inverse square, harmonic oscillator and pure Coulomb potentials. The energy eigenvalues and their corresponding wave functions are determined.

International Journal of Modern Physics A•Oct 30, 2024•2 citations

Wave Mechanics in Quantum Phase Space: Harmonic Oscillator

Jun Lu

In this paper, we solve the rigorous solutions of the stationary Schrödinger equations for the harmonic oscillator within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. We obtain the phase-space eigenfunctions of the three-dimensional isotropic harmonic oscillator in rectangular and spherical coordinate systems, and discuss the relationship between the eigenfunctions of the two coordinate systems. We also extend the "Fourier-like" projection transformations of the phase-space wave function to three-dimensional systems, and obtain the eigenfunctions in position and momentum representation through the transformations of the eigenfunction in the phase-space representation.

Physica Scripta•Jan 1, 2004•4 citations

Ladder operators for some spherically symmetric potentials in quantum mechanics

J. D. Newmarch, RAYMUND M. GOLDING

The energy levels of the free field, Coulomb potential, and the three-dimensional harmonic oscillator are found using the Dirac operator formalism by the construction of suitable ladder operators. The degeneracy of each level is also discussed.

American Journal of Physics•Jun 1, 1978•17 citations
Abstract The separability of the Schrödinger equation for harmonic oscillators in D dimensions and in different coordinate systems (Cartesian, circular, spherical) makes possible the construction of common generating functions for the complete harmonic oscillator wave functions in the corresponding dimensions and coordinates. Explicit forms of such generating functions and their series expansions are presented, and one of their applications is illustrated through the evaluation of transformation brackets. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
In this paper, we solve the rigorous solutions of the stationary Schrödinger equations for the harmonic oscillator within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. We obtain the phase-space eigenfunctions of the three-dimensional isotropic harmonic oscillator in rectangular and spherical coordinate systems, and discuss the relationship between the eigenfunctions of the two coordinate systems. We also extend the "Fourier-like" projection transformations of the phase-space wave function to three-dimensional systems, and obtain the eigenfunctions in position and momentum representation through the transformations of the eigenfunction in the phase-space representation.