Isotropic harmonic oscillator plus inverse quadratic potential in N-dimensional spaces

الملخص EN

Some aspects of the N-dimensional isotropic harmonic plus inverse quadratic potential are discussed.

The hyperradial equation for isotropic harmonic oscillator plus inverse quadratic potential is solved by transformation into the confluent hypergeometric equation to obtain the normalized hyperradial solution.

Together with the hyperangular solutions (hyperspherical harmonics), these form the complete energy eigenfunctions of the N-dimensional isotropic harmonic oscillator plus inverse quadratic potential and the energy eigenvalues are also obtained.

These are dimensionally dependent.

The dependence of the radial solution on the dimensions or the potential strength and the degeneracy of the energy levels are discussed