We study the Wigner Function in non-commutative quantum mechanics. By solving the time independent Schrödinger 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.
The quantum harmonic oscillator is a basic model for many complex ones.After integration,the Wigner function of quantum harmonic oscillator can be expressed by a simple form,which can be used to solve many related problems.This paper has placed the harmonic oscillator in non-commutative phase space,and studied the Wigner function of two-dimensional charged harmonic oscillator in electric field.The results show that when the non-commutative parameter is zero,the Wigner function of two-dimensional charged harmonic oscillator is equivalent to its form in commutative space.