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A simple method has been introduced to furnish the equilibrium solution ofthe Wigner equation for all order of the quantum correction. This processbuilds up a recursion relation involving the coefficients of the differentpower of the velocity. The technique greatly relies upon the proper guess workof the trial solution and is different from the Wigner s original work. Thesolution is in a compact exponential form with a polynomial of velocity in theargument and returns the Wigner s form when expansion of the exponential factoris carried out. The study keeps its importance in studying various close aswell as open quantum mechanical system. In addition, this solution may beemployed to obtain the non equilibrium one particle wigner distribution in therelaxation-time approximation and under near-equilibrium conditions.

A simple method to obtain the equilibrium solution of Wigner-Boltzmann Equation with all higher order quantum corrections