@article {10.3844/ajassp.2005.376.382,
article_type = {journal},
title = {An Algebraic Approach to the Harmonic Oscillator Plus an Inverse Square Potential in Three Dimensions},
author = {Dong, Shi-Hai and Lozada-Cassou, M.},
volume = {2},
year = {2005},
month = {Jan},
pages = {376-382},
doi = {10.3844/ajassp.2005.376.382},
url = {https://thescipub.com/abstract/ajassp.2005.376.382},
abstract = {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.},
journal = {American Journal of Applied Sciences},
publisher = {Science Publications}
}