I would like to understand phase space better, spec. in relation to the quantum Liouville theorem. Can anyone point me to a decent online resource? I am most interested in conceptual understanding to begin with.(adsbygoogle = window.adsbygoogle || []).push({});

Liouville's theorem says that if you follow a point in phase space, the number of points surrounding that point will always be the same. Or, equivalently, "The distribution function is constant along any trajectory in phase space."

In the case of a quantum density matrix, what does the phase space represent? The various possible states and their probabilities?

What, then, is an intuitive interpretation of the "points in phase space", and their "spacing"?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Phase space and the quantum Liouville theorem

**Physics Forums | Science Articles, Homework Help, Discussion**