Day 157: Phase Space — The Geometric Arena of Hamiltonian Mechanics

Learning Objectives

• •Define phase space as a 2n-dimensional manifold and understand its geometric structure
• •Explain why phase space trajectories cannot cross and derive the existence/uniqueness theorem
• •Construct and interpret phase portraits for standard mechanical systems
• •Classify fixed points (centers, saddles) and understand their stability
• •Identify separatrices and explain their physical significance
• •Connect phase space concepts to quantum mechanics via the Wigner function and uncertainty principle

Today's Schedule (7 hours)