1203.2359 (J. Sadeghi et al.)

Superalgebra and Harmonic Oscillator with Constant Positive Curvature    [PDF]

J. Sadeghi, H. Moayyeri

We study the Schr\"odinger equation for the isotropic oscillator in three-dimensional space with constant positive curvature. So, the description of solutions for the corresponding Schr\"odinger equation based on the spherical coordinates. By comparing the Schr\"odinger equation of harmonic oscillator in constant positive curvature to the associated Jacobi polynomial, we obtain the energy spectrum and wave function. The associated Jacobi equation help us to factorize the Schr\"odinger equation for the isotropic oscillator. The first order equation from factorization method lead us to define the raising and lowering operators. These operators are supersymmetric structure related to the Hamiltonian partner, thus we obtain the corresponding supercharges.

View original: http://arxiv.org/abs/1203.2359