Abstract
A nonlinear model representing the quantum harmonic oscillator on the three-dimensional spherical and hyperbolic spaces, S3κ (κ > 0) and H3k (κ < 0), is studied. The curvature κ is considered as a parameter and then the radial Schrödinger equation becomes a κ-dependent Gauss hypergeometric equation that can be considered as a κ-deformation of the confluent hypergeometric equation that appears in the Euclidean case. The energy spectrum and the wavefunctions are exactly obtained in both the three-dimensional sphere S3κ (κ > 0) and the hyperbolic space H3k (κ < 0). A comparative study between the spherical and the hyperbolic quantum results is presented.
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