Addendum to An update on the classical and quantum harmonic oscillators on the sphere and the hyperbolic plane in polar coordinates

TL;DR

This paper extends classical and quantum harmonic oscillator models on curved surfaces by adding an isotonic term, providing new solutions for oscillators on the sphere and hyperbolic plane.

Contribution

It introduces an isotonic term into existing models, offering extended solutions for harmonic oscillators on curved geometries.

Findings

Extended solutions for oscillators on curved surfaces.

Inclusion of isotonic term modifies the potential and solutions.

Provides a broader framework for quantum and classical oscillators.

Abstract

The classical and quantum solutions of a nonlinear model describing harmonic oscillators on the sphere and the hyperbolic plane, derived in polar coordinates in a recent paper [Phys.\ Lett.\ A 379 (2015) 1589], are extended by the inclusion of an isotonic term.