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 Anhui Normal University

ENERGY RELATION BETWEEN THREE-DIMENSIONAL HARMONIC OSCILLATOR AND HYDROGEN ATOM IN UBVERSE SQUARE POTENTIAL

Fan Li-fang

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

In terms of SU(1,1) algebra, the eigen equations of three-dimensional Harmonic Oscillator and hydrogen atom in inverse square potential are counterchanged the same equations in form. Then the relation of energy between them is found.

Related papers

Energy and wave function of the three-dimensional harmonic oscillator and hydrogen atom

Zhao Su-qin

Through the counterchanges of two methodologies of coordinates and special equations,the eigen equations of the three-dimensional harmonic oscillator and hydrogen atom are converted into the same equations in form.Then the relationship between the energy and wave function of the three-dimensional harmonic oscillator and hydrogen atom is given.

Journal of Qinghai Normal University•Jan 1, 2005•0 citations

ENERGY AND WAVE FUNCTION OF THE TWO DIMENSIONAL HARMONIC OSCILLTOR AND HYDROGEN ATOM

Hao Chen

By the coordinates counterchange,the relationship between energy and wave function of Two dimensional Harmonic Oscillator and Hydrogen Atom are found.

Journal of South China Normal University•Jan 1, 2004•0 citations

The Relationship between the Two-dimensivnal Hydrogen Atom and the Two-dimensional Harmonic oscillator

Yang Liu

In this paper,We work out the relationship between the energy eigenfunction,the energy eigenvalues of the two-dimensional hydrogen atom and those of the two-dimensional harmonic oscillator in terms of su(1,1) algebra.The their coordinate trans formation is worked out.

Journal of Yiyang Teachers College•Jan 1, 2001•0 citations

ALGEBRAIC SOLUTION TO THE ENERGY LEVEL AND WAVE FUNCTION OF ONE-DIMENSIONAL HARMONIC OSCILLATOR

Changrong Wang

In the research of one-dimensional harmonic oscillaton as the object in Heisenberg's picture.We have got two kinds of solutions of its energy level and wave fanction by algebraic approach of using matrix mechanics and factorization method.

Journal of Hubei Institute for Nationalities•Jan 1, 2000•0 citations

AN ALGEBRAIC APPROACH TO A HARMONIC OSCILLATOR PLUS AN INVERSE SQUARE POTENTIAL IN TWO DIMENSIONS

Shi‐Hai Dong, Guo-Hua Sun, Marcelo Lozada‐Cassou

The exact solutions of the Schrödinger equation with a harmonic oscillator plus an inverse square potential are obtained in two dimensions. We construct the ladder operators directly from the radial wave functions and find that these operators satisfy the commutation relations of an SU (1, 1) group. We obtain the explicit expressions of the matrix elements for some related functions ρ and [Formula: see text] with ρ = r2. We also explore another symmetry between the eigenvalues E(r) and E(ir) by substituting r→ir.

International Journal of Modern Physics A•Sep 30, 2005•11 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
The exact solutions of the Schrödinger equation with a harmonic oscillator plus an inverse square potential are obtained in two dimensions. We construct the ladder operators directly from the radial wave functions and find that these operators satisfy the commutation relations of an SU (1, 1) group. We obtain the explicit expressions of the matrix elements for some related functions ρ and [Formula: see text] with ρ = r2. We also explore another symmetry between the eigenvalues E(r) and E(ir) by substituting r→ir.
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.