Day 163: Liouville's Theorem — Conservation of Phase Space Volume

Learning Objectives

• •State and prove Liouville's theorem using multiple approaches (divergence, Jacobian, geometric)
• •Explain why Hamiltonian flow is analogous to incompressible fluid flow
• •Write and interpret the Liouville equation for phase space density evolution
• •Connect Liouville's theorem to the von Neumann equation in quantum mechanics
• •Apply Liouville's theorem to statistical mechanics and plasma physics
• •Understand why symplectic integrators preserve phase space structure

Today's Schedule (7 hours)