# Wigner Functions for harmonic oscillator in noncommutative phase space

## TL;DR

This paper derives the Wigner Function for the harmonic oscillator within non-commutative quantum mechanics, considering both non-commutative space and phase space, providing a detailed analysis of quantum states in these frameworks.

## Contribution

It presents the first explicit calculation of the Wigner Function for the harmonic oscillator in non-commutative space and phase space, extending quantum phase space analysis.

## Key findings

- Wigner Function for harmonic oscillator in NC space derived
- Wigner Function for harmonic oscillator in NC phase space derived
- Provides insights into quantum states in non-commutative frameworks

## Abstract

We study the Wigner Function in non-commutative quantum mechanics. By solving the time independent Schr\"{o}dinger equation both on a non-commutative (NC) space and a non-commutative phase space, we obtain the Wigner Function for the harmonic oscillator on NC space and NC phase space respectively.