An update on the classical and quantum harmonic oscillators on the sphere and the hyperbolic plane in polar coordinates
Mathematical Physics
2015-05-20 v2 math.MP
Exactly Solvable and Integrable Systems
Classical Physics
Quantum Physics
Abstract
A simple derivation of the classical solutions of a nonlinear model describing a harmonic oscillator on the sphere and the hyperbolic plane is presented in polar coordinates. These solutions are then related to those in cartesian coordinates, whose form was previously guessed. In addition, the nature of the classical orthogonal polynomials entering the bound-state radial wavefunctions of the corresponding quantum model is identified.
Keywords
Cite
@article{arxiv.1411.4853,
title = {An update on the classical and quantum harmonic oscillators on the sphere and the hyperbolic plane in polar coordinates},
author = {C. Quesne},
journal= {arXiv preprint arXiv:1411.4853},
year = {2015}
}
Comments
13 pages, 2 figures, published version