# A Note on Deformed Ladder Operators for Noncommutative Morse Oscillator

## TL;DR

This paper develops deformed ladder operators for the 2D Morse oscillator, introducing noncommutative properties into quantum mechanics, with potential applications in quantum chemistry and noncommutative quantum theories.

## Contribution

It presents a novel method to deform Morse ladder operators to incorporate noncommutative geometry into the 2D Morse potential framework.

## Key findings

- Deformed ladder operators exhibit noncommutative spatial properties.
- The noncommutative Hamiltonian is explicitly constructed.
- The approach extends Morse oscillator analysis to noncommutative quantum mechanics.

## Abstract

Morse oscillator is one of the known solvable potentials which attracts many applications in quantum mechanics especially in quantum chemistry. One of the interesting results of this study is the generation of ladder operators for Morse potential. The operators are a representation of the shifting energy levels of the states exhibited by the wavefunction. From this result, we manipulate and deform the operators in such a way that it gives a noncommutative property to promote noncommutative quantum mechanics (NCQM). The resultant NC feature can be shown in the spatial coordinates and finally the Hamiltonian. In this study, we consider two-dimensional Morse potential where the ladder operators are in the form of the corresponding 2D Morse.