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

American Journal of Applied Sciences

M. Lozada-Cassou¹  Shi-Hai Dong¹ 

关键词: Inverse Square Interaction;    Ladder Operators;    SU (1;    1) Group;    Matrix Elements;   

DOI  :  10.3844/ajassp.2005.376.382

学科分类：自然科学（综合）

来源: Science Publications

【 摘 要 】

The eigenfunctions and eigenvalues of the three-dimensional Schrödinger equation with aharmonic oscillator plus an inverse square interaction are obtained. A realization of the ladderoperators for the wave functions is studied. It is found that these operators satisfy the commutationrelations of an SU(1,1) group. The closed analytical expressions for the matrix elements of differentfunctions ρ and ρd/dρwith ρ = r ² are evaluated. Another hidden symmetry explores the relationsbetween the eigenvalues and eigenfunctions for substituting r

【 授权许可】

Unknown