Day 162: Canonical Transformations — The Symmetry Group of Hamiltonian Mechanics

Learning Objectives

• •Define canonical transformations and explain why they preserve Hamilton's equations
• •Derive and apply all four types of generating functions (F₁, F₂, F₃, F₄)
• •Prove that the Jacobian matrix of a canonical transformation is symplectic
• •Verify that transformations preserve Poisson brackets
• •Construct canonical transformations for specific physical problems
• •Connect canonical transformations to unitary transformations in quantum mechanics

Today's Schedule (7 hours)