Liouville equation

Quantum Liouville equation

The analog of Liouville equation in quantum mechanics describes the time evolution of a mixed state. Canonical quantization yields a quantum-mechanical version of this theorem, the Von Neumann equation. This procedure, often used to devise quantum analogues of classical systems, involves describing a classical system using Hamiltonian mechanics. Classical variables are then re-interpreted as quantum operators, while Poisson brackets are replaced by commutators.

— Wikipedia on Liouville’s theorem (Hamiltonian)

2014.09.28 Sunday ACHK