American Journal of Applied Sciences

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

Shi-Hai Dong and M. Lozada-Cassou

DOI : 10.3844/ajassp.2005.376.382

American Journal of Applied Sciences

Volume 2, Issue 1

Pages 376-382


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.


© 2005 Shi-Hai Dong and M. Lozada-Cassou. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.