Quantum Physics lives and breathes in Phase Space

Quantum physical wave functions (or density matrices) describe the state of a quantum system. They
are complex valued. This makes visualising and interpreting their features hard.

There is an alternative: Wigner's representation of quantum physics, in this representation the
state is described by a real valued Wigner distribution, this makes visualising and interpreting
the features of quantum states easier.

Additionally, the Wigner representation describes the dynamics of the quantum state by a continuity
equation for the current of the Wigner distribution. Only the Wigner representation has such a
current and therefore only in this representation is it possible to plot the current and see how it
moves the distribution.

I will introduce distributions in classical phase space and their dynamics described by the
classical (Liouvillian) phase space continuity equation. Then I will describe the (well known,
regular) Schroedinger-von Neumann representation and explain how a Fourier transform maps it to the
Wigner representation and its continuity equation.

I will supplement my presentation by many images, and also some videos to demonstrate how the Wigner
representation gives us visualisations of quantum systems and their dynamics.