Transformation of Differential Equations Into Phase Space

Abstract

Suppose we want to obtain the Wigner distribution of a function $\varphi{(x)}$ which is the solution of a linear differential equation

$$ a_{n}\frac{d^{n}\varphi(x)}{dx^{n}} + a_{n-1}\frac{d^{n-1}\varphi(x)}{dx^{n-1}}\;\cdots\; + a_{1}\frac{d\varphi(x)}{dx} + a_{0}\varphi(x) = f(x)$$

(10.1)

.