Jérémie Joudioux (AEI)
The Wigner transform was introduced at the beginning of the 30s to understand quantum corrections to classical statistical mechanics. It has then been used in optics to perform analysis in phase space of the propagation of a signal. In this talk, I will introduce the Wigner transform, and explain its basic properties. I will then explain how to relate the equation of propagation of a signal, to the transport equation satisfied by its Wigner distribution function. In the last part, I will explain how the Wigner transform can be used to formalise the WKB approximation.