The Wigner distribution for ordinary linear differential equations and wave equations

A new method is presented to study systems governed by ordinary linear differential equations and partial differential equations whose solutions are waves. We show that one can obtain a differential equation for the Wigner distribution of the solution of a dynamical equation of evolution. As an example we derive in a new way the equation governing the Wigner distribution for the Schrodinger equation. We also consider differential equations where the forcing terms are random processes