The quantum harmonic oscillator on the sphere and the hyperbolic plane: kappa-dependent formalism, polar coordinates, and hypergeometric functions
Oct, 2007Citations per year
Abstract: (AIP)
A nonlinear model representing the quantum harmonic oscillator on the sphere and the hyperbolic plane is solved in polar coordinates ( r , ϕ ) by making use of a curvature-dependent formalism. The curvature κ is considered as a parameter and then the radial Schrödinger equation becomes a κ -dependent Gauss hypergeometric equation. The energy spectrum and the wave functions are exactly obtained in both the sphere S 2 ( κ > 0 ) and the hyperbolic plane H 2 ( κ < 0 ) . A comparative study between the spherical and the hyperbolic quantum results is presented.- harmonic oscillators
- nonlinear dynamical systems
- Schrodinger equation
- wave functions
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