  A Cumulant based method has been introduced to extract quantum corrections in
distribution function with the equilibrium Wigner-Boltzmann equation. It is
shown that unlike the moment expansion used in hydrodynamic model, cumulant
expansion converges much faster when distribution function is closed to
Maxwellian with only first three cumulants are non-zero. In this case, quantum
corrections higher than first order can be extracted mainly by lowest three
cumulants and odd number derivatives of potential function. This method also
provides a new way to determine the distribution function with Maxwellian form
and study the role of potential function in quantum correction field.
