TY - JOUR AU - Dong, Shi-Hai AU - Lozada-Cassou, M. PY - 2005 TI - An Algebraic Approach to the Harmonic Oscillator Plus an Inverse Square Potential in Three Dimensions JF - American Journal of Applied Sciences VL - 2 IS - 1 DO - 10.3844/ajassp.2005.376.382 UR - https://thescipub.com/abstract/ajassp.2005.376.382 AB - 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.