# Classical ladder functions for Rosen-Morse and curved Kepler-Coulomb systems

## TL;DR

This paper introduces a new method for deriving ladder functions in classical mechanics, specifically applied to curved Kepler-Coulomb and Rosen-Morse II systems, enabling analysis of their motion.

## Contribution

A novel approach using product of factor functions to find ladder functions in classical systems, applied to previously uncharacterized curved Kepler-Coulomb and Rosen-Morse II systems.

## Key findings

- Derived ladder functions for curved Kepler-Coulomb system
- Derived ladder functions for Rosen-Morse II system
- Applied ladder functions to analyze system motion

## Abstract

Ladder functions in classical mechanics are defined in a similar way as ladder operators in the context of quantum mechanics. In the present paper, we develop a new method for obtaining ladder functions of one dimensional systems by means of a product of two `factor functions'. We apply this method to the curved Kepler-Coulomb and Rosen-Morse II systems whose ladder functions were not found yet. The ladder functions here obtained are applied to get the motion of the system.