In the case of a polyatomic molecule, there is a mapping between independent one-dimensional vibrational modes and the Cartesian coordinates and their corresponding momentums of atoms. The linear displacement of the atoms in the Cartesian coordinates r from their equilibrium positions (r e ) can be related to the vector of displacements of vibrational modes ξ through the matrix of the mode shapes L: R = (r -r e ) = Lξ. A similar relation connects the Cartesian momentums of the atoms P = -ih∂ R to the momentums of the independent modes p = -ih∂ ξ : P = L -1 p. The Wigner function for ξ and p is just a product of the one-dimensional quasi-probability distributions (Equation ), and it can be written as