The quantum harmonic oscillator on the sphere and the hyperbolic plane: kappa-dependent formalism, polar coordinates, and hypergeometric functions

Oct, 2007
13 pages
Published in:
  • J.Math.Phys. 48 (2007) 102106

Citations per year

201120152019202320252014
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
Loading ...