The Liouville's theorem (Hamiltonian) reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Liouville's theorem (Hamiltonian)

In Hamiltonian mechanics, Liouville's theorem predicts how probability distributions evolve under time evolutions.

An interesting corollary of this theorem is that time evolutions are area/volume-preserving.

There is a quantum-mechanical version of this theorem in the Schrödinger picture.

where ρ is the density matrix.

See also Joseph Liouville.

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