AN ALGEBRAIC APPROACH TO A HARMONIC OSCILLATOR PLUS AN INVERSE SQUARE POTENTIAL IN TWO DIMENSIONS-Reference-Cited by-同舟云学术

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

Published:2005-09-30 Issue:24 Volume:20 Page:5663-5670
ISSN:0217-751X
Container-title:International Journal of Modern Physics A
language:en
Short-container-title:Int. J. Mod. Phys. A

Author:

DONG SHI-HAI¹,SUN GUO-HUA²,LOZADA-CASSOU M.¹

Affiliation:

1. Programa de Ingeniería Molecular, Instituto Mexicano del Petróleo, Lázaro Cárdenas 152, 07730 México, D.F., Mexico

2. Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, UNAM, A. P. 20-726, Del. Alvaro Obregón, México D.F., 01000, Mexico

Abstract

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0217751X05022305

Reference17 articles.

1. Summary of the activities of the structure function working group

2. The Factorization Method

3. Closed‐form expressions of matrix elements and eigenfunctions from ladder‐operator considerations

4. Ladder operators for the Morse potential

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